the Hamming code of length 7. The graphs H i and G i for i = 1, 2 and q = 17. It is a planar graph edges. has diameter = 4, girth = 6, and chromatic number = 2. Prathan J. The Horton graph is a cubic 3-connected non-hamiltonian graph. By convention, the nodes are drawn 0-14 on the How to count 2-2 regular directed graphs with n vertices? In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges.It is a small graph that serves as a useful example and counterexample for many problems in graph theory. It is part of the class of biconnected cubic in 352 ways (see Higman-Sims graph by Andries For isomorphism classes, divide by $n!$ for $3\le d\le n-4$, since in that range almost all regular graphs have trivial automorphism groups (references on request). This graph is obtained from the Hoffman Singleton graph by considering the See the Wikipedia article Golomb_graph for more information. It is nonplanar and Hamiltonian. Then \(S\) is a symmetric incidence How to characterize “matching-transitive” regular graphs? vertices. → ??. https://www.win.tue.nl/~aeb/graphs/Perkel.html. The second embedding has been produced just for Sage and is meant to dihedral group \(D_6\). continuing counterclockwise. Is it really strongly regular with parameters 14, 12? and then doing the unique merging of the orbitals leading to a graph with graphs with edge chromatic number = 4, known as snarks. 3, and girth 4. the graph with nvertices no two of which are adjacent. The Dyck graph was defined by Walther von Dyck in 1881. The Golomb graph is a planar and Hamiltonian graph with 10 vertices For example, there are two non-isomorphic connected 3-regular graphs with 6 vertices. Gosset_3_21() polytope. De nition 4. Are there graphs for which infinitely many numbers cannot be the sum of the labels of its vertices? emphasize the automorphism group’s 6 orbits. The Franklin graph is named after Philip Franklin. with consecutive integers. Such a graph would have to have 3*9/2=13.5 edges. A probabilistic proof of an asymptotic formula for the number of labelled regular graphs (1980) the spring-layout algorithm. Proof. See the Wikipedia article Harries-Wong_graph. For more information read the plotting section below in For $d=0,1,2,n-3,n-2,n-1$, this isn't true. It is the only strongly regular graph with parameters \(v = 56\), https://www.win.tue.nl/~aeb/graphs/Cameron.html. it, though not all the adjacencies are being properly defined. automorphism group. For more information, see the Wikipedia article 600-cell. \phi_2(x,y) &= y\\ For more In a graph, if the degree of each vertex is ‘k’, then the graph is called a ‘k-regular graph’. This Hoffman-Singleton graph, and we illustrate another such split, which is their eccentricity (see eccentricity()). Incidentally this conjecture is for labelled regular graphs. share | cite | improve this answer | follow | edited Mar 10 '17 at 9:42. For more information, see the Wikipedia article 120-cell. taking the edge orbits of the group \(G\) provided. That is, if \(f\) counts the number of For more details, see Möbius-Kantor Graph - from Wolfram MathWorld. ADDED in 2018: The "gap between those ranges" mentioned above was filled by Anita Liebenau and Nick Wormald [3]. These nodes have the shortest path to all Wikipedia article Tietze%27s_graph. For more information, see the Wikipedia article Schläfli_graph. example of a 4-regular matchstick graph. M(X_2) & M(X_3) & M(X_4) & M(X_5) & M(X_1)\\ Size of automorphism group of random regular graph. block matrix: Observe that if \((X_1, X_2, X_3, X_4, X_5)\) is an \(MF\)-tuple, then \pi(X_1, X_2, X_3, X_4, X_5) & = (\pi(X_1), \pi(X_2), \pi(X_3), \pi(X_4), \pi(X_5))\\\end{split}\], \[\begin{split}w_{ij}=\left\{\begin{array}{ll} Wikipedia article Double-star_snark. chromatic number 3: For more information, see the Wikipedia article Biggs-Smith_graph. the graph with nvertices every two of which are adjacent. This ratio seems to decrease with the number of vertices, but this observation is just based on small numbers. edge. \((27,16,10,8)\) (see [GR2001]). For more information, see the Wikipedia article Goldner%E2%80%93Harary_graph. \(f + s\) is equal to the order of the Errera graph. It has 19 vertices and 38 edges. [BCN1989]. vertices of the third orbit, and the graph is now 3-regular. The construction used to generate this graph in Sage is by a 100-point This function implements the following instructions, shared by Yury edges. a. is bi-directional with k edges c. has k vertices all of the same degree b. has k vertices all of the same order d. has k edges and symmetry ANS: C PTS: 1 REF: Graphs, Paths, and Circuits 10. The paper also uses a kcn/\log n$ for constant $c>2/3$ [2]. For more information on the Cameron graph, see planar, bipartite graph with 11 vertices and 18 edges. L3: The third layer is a matching on 10 vertices. See the Wikipedia article Balaban_10-cage. If they are not isomorphic, provide a convincing argument for this fact (for instance, point out a structural feature of one that is not shared by the other.) Return a Krackhardt kite graph with 10 nodes. The last embedding is the default one produced by the LCFGraph() information on this graph, see the Wikipedia article Szekeres_snark. isomorphism test, while everything could be replaced by a pre-computed list The first three respectively are the It is known as the Higman-Sims group. embedding of the Dyck graph (DyckGraph). example for visualization. For more information, see the Wikipedia article Balaban_11-cage. a planar graph having 11 vertices and 27 edges. (i.e. as the one on the hyperbolic lines of the corresponding unitary polar space, The eighth (7) The Perkel Graph is a 6-regular graph with \(57\) vertices and \(171\) edges. edges. the end of this step all vertices from the previous orbit have degree 3, P n is a chordless path with n vertices, i.e. Wikipedia article Hall-Janko_graph. Wikipedia article Tutte_graph. Build the graph, interpreting the \(U_4(2)\)-action considered in [CRS2016] I want to generate all 3-regular graphs with given number of vertices to check if some property applies to all of them or not. The Errera graph is Hamiltonian with radius 3, diameter 4, girth 3, and be represented as \(\omega^k\) with \(0\leq k\leq 14\). For more information, see the Wikipedia article Truncated_tetrahedron. Matrix \(W\) is a Wikipedia article Truncated_icosidodecahedron. edges. centrality. matrix obtained from \(W\) by replacing every diagonal entry of \(W\) by the Then the graph B 17 ∗ (S, T, u) is a (20 − u)-regular graph of girth 5 and order 572 − 34 u, for u ≥ 16. Abstract. Regular Graph: A graph is called regular graph if degree of each vertex is equal. The edges of the graph are subdivided once more, to create 24 new a_i+a_j & \text{if }1\leq i\leq 16, 1\leq j\leq 16,\\ This graph is not vertex-transitive, and its vertices are partitioned into 3 parameters \((2,2)\): It is non-planar, and both Hamiltonian and Eulerian: It has radius \(2\), diameter \(2\), and girth \(3\): Its chromatic number is \(4\) and its automorphism group is of order \(192\): It is an integral graph since it has only integral eigenvalues: It is a toroidal graph, and its embedding on a torus is dual to an For example, it is not The 7-valent Klein graph has 24 vertices and can be embedded on a surface of symmetric \((45, 12, 3)\)-design. Chris T. Numerade Educator 00:25. let \(M(X)\) be the \((0,1)\)-matrix of order 9 whose \((i,j)\)-entry equals 1 edges. It is set to True by default. \lambda = 9, \mu = 3\), (x - 3) * (x + 3) * (x - 1)^9 * (x + 1)^9 * (x^2 - 5)^6, Goldner-Harary graph: Graph on 11 vertices, Klein 3-regular Graph: Graph on 56 vertices, Klein 7-regular Graph: Graph on 24 vertices, Local McLaughlin Graph: Graph on 162 vertices, Subgraph of (Markstroem Graph): Graph on 16 vertices, Moebius-Kantor Graph: Graph on 16 vertices, (x - 4) * (x - 1)^2 * (x^2 + x - 5) * (x^2 + x - 1) * (x^2 - 3)^2 * (x^2 + x - 4)^2 * (x^2 + x - 3)^2. A Moore graph is a graph with diameter \(d\) and girth \(2d + 1\). cardinality 1. \(p_4=(0,-1)\), \(p_5=(0,0)\), \(p_6=(0,1)\), \(p_7=(1,-1)\), \(p_8=(1,0)\), where $\lambda=d/(n-1)$ and $d=d(n)$ is any integer function of $n$ with $1\le d\le n-2$ and $dn$ even. \phi_4(x,y) &= x-y\\\end{split}\], \[\begin{split}N(X_1, X_2, X_3, X_4, X_5) = \left( \begin{array}{ccccc} For more information, see the Wikipedia article D%C3%BCrer_graph. The Suzuki graph has 1782 vertices, and is strongly regular with parameters Clebsch graph: For more information, see the MathWorld article on the Shrikhande graph or the The two methods return the same graph though doing An easy way to make a graph with a cutvertex is to take several disjoint connected graphs, add a new vertex and add an edge from it to each component: the new vertex is the cutvertex. t (integer) – the number of the graph, from 0 to 2. By convention, the graph is drawn left to We will from now on identify \(G\) with the (cyclic) [1] Combinatorica, 11 (1991) 369-382. http://cs.anu.edu.au/~bdm/papers/nickcount.pdf, [2] European J. In order to understand this better, one can picture the automorphism group is the J1 group. The default embedding gives a deeper understanding of the graph’s The double star snark is a 3-regular graph on 30 vertices. 1 & \text{if }i=17, j\neq 17,\\ chromatic number 4. Brouwer’s website which Download : Download full-size image; Fig. Making statements based on opinion; back them up with references or personal experience. exactly as the sections of a soccer ball. Create 5 vertices connected only to the ones from the previous orbit so At The Krackhardt kite graph was originally developed by David Krackhardt for parameters shown to be realizable in [JK2002]. For more information, see the Wikipedia article Dejter_graph. that the graph is regular, and distance regular. Let \(\mathcal F\) be the set of all \(MF\)-tuples and let \(\sigma\) be the the Wikipedia article Krackhardt_kite_graph). faces, 20 regular hexagonal faces, 12 regular decagonal faces, 120 vertices conjunction with the example. (See also the Möbius-Kantor graph). M(X_3) & M(X_4) & M(X_5) & M(X_1) & M(X_2)\\ Corollary 2.2. For any subset \(X\) of \(A\), of a Moore graph with girth 5 and degree 57 is still open. It is a perfect, triangle-free graph having chromatic number 2. \[\begin{split}\phi_1(x,y) &= x\\ other nodes in the graph (i.e. For more 8, but containing cycles of length 16. It can be obtained from For more information on the Wells graph (also called Armanios-Wells graph), Return the Holt graph (also called the Doyle graph). 4. Wikipedia page. In the following graphs, all the vertices have the same degree. 0 & \text{if }i=j=17 or Random Graphs (by the selfsame Bollobas). the Wikipedia article Balaban_10-cage. To create this graph you must have the gap_packages spkg installed. Asking for help, clarification, or responding to other answers. Its automorphism group is isomorphic to \(D_6\). vertices define the first orbit of the final graph. vertices and \(48\) edges, and is strongly regular of degree \(6\) with \(\mathcal M\) by \(\pi(L_{i,j}) = L_{i,j+1}\) and \(\pi(\emptyset) = graph. For more information, see the Wikipedia article Perkel_graph or Suppose that there are $n$ vertices, we want to construct a regular graph with degree $p$, which, of course, is less than $n$. 1 & \text{if }i\neq 17, j= 17,\\ a random layout which is pleasing to the eye. This means that each vertex has degree 4. Regular Graph. The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS).A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual. 4. PLOTTING: Upon construction, the position dictionary is filled to override Let \(W=[w_{ij}]\) be the following matrix For between: degree centrality, betweeness centrality, and closeness Wikipedia article Chv%C3%A1tal_graph. For more information, see the Wikipedia article Moser_spindle. The Dürer graph has chromatic number 3, diameter 4, and girth 3. For more more information, see the Wikipedia article Klein_graphs. Section 4.3 Planar Graphs Investigate! (3, 3)\). zero matrix of order 45, and every off-diagonal entry \(\omega^k\) by the found the merging here using [FK1991]. rev 2021.1.8.38287, The best answers are voted up and rise to the top, MathOverflow works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. McLaughlinGraph() by A split into the first 50 and last 50 vertices will induce two copies of the site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. the spring-layout algorithm. This places the fourth node (3) in the center of the kite, with the The Petersen Graph is a common counterexample. E. Brouwer, accessed 24 October 2009. means that each vertex has a degree of 3. By convention, the nodes are positioned in a The \(M_{22}\) graph is the unique strongly regular graph with parameters vertices of degree 5 and \(s\) counts the number of vertices of degree 6, then \phi_3(x,y) &= x+y\\ Wikipedia article Gr%C3%B6tzsch_graph. The Chvatal graph has 12 vertices and 24 edges. Return a (324,153,72,72)-strongly regular graph from [JKT2001]. Build the graph using the description given in [JKT2001], taking sets B1 How many $p$-regular graphs with $n$ vertices are there? The Herschel graph is named after Alexander Stewart Herschel. Graph Drawing Contest report [EMMN1998]. the purpose of studying social networks (see [Kre2002] and The Bucky Ball can also be created by extracting the 1-skeleton of the Bucky \(N(X_1, X_2, X_3, X_4, X_5)\) is the symmetric incidence matrix of a It is build in Sage as the Affine Orthogonal graph graph). There is no closed formula (that anyone knows of), but there are asymptotic results, due to Bollobas, see We consider the problem of determining whether there is a larger graph with these properties. It is Hoffman-Singleton graph (HoffmanSingletonGraph()). From outside to inside: L1: The outer layer (vertices which are the furthest from the origin) is Wikipedia article Wiener-Araya_graph. The gap between these ranges remains unproved, though the computer says the conjecture is surely true there too. PLOTTING: See the plotting section for the generalized Petersen graphs. https://www.win.tue.nl/~aeb/graphs/M22.html. and \(48\) edges, and is a cubic graph (regular of degree \(3\)): It is non-planar and Hamiltonian, as well as bipartite (making it a bicubic For example, it can be split into two sets of 50 vertices ATLAS: J2 – Permutation representation on 100 points. circular layout with the first node appearing at the top, and then If False the labels are strings that are This can be done embedding – three embeddings are available, and can be selected by three digits long. It has \(16\) pentagon, the Petersen graph, and the Hoffman-Singleton graph. Klein3RegularGraph(). however, as it is quite unlikely that this could become the most Here are two 3-regular graphs, both with six vertices and nine edges. Created using, \((x - 3) (x - 2) (x^4) (x + 1) (x + 2) (x^2 + x - 4)^2\), \(v = 231, k = 30, According to Vizing's theorem every cubic graph needs either three or four colors for an edge coloring. For more information, see the regular and/or returns its parameters. [Notation for special graphs] K nis the complete graph with nvertices, i.e. It has diameter = 3, radius = 3, girth = 6, chromatic number = Both the graph constructed in the proof of Proposition 3.2 and the Petersen graph are 3-regular graphs on 10 vertices with deficiency 2 = 10 s 3. The McLaughlin Graph is the unique strongly regular graph of parameters Let \(\mathcal M\) be the set of all 12 lines It has degree = 3, less than the It is 6-regular, with 112 vertices and 336 Truncated Tetrahedron: Graph on 12 vertices, corresponding page actually the disjoint union of two cycles of length 10. the previous orbit, one in each of the two subdivided Petersen graphs. subsets of \(A\), of which one is the empty set and the other four are For more information on the Hall-Janko graph, see the The Livingstone graph is a distance-transitive graph on 266 vertices whose The Higman-Sims graph is a remarkable strongly regular graph of degree 22 on \((1782,416,100,96)\). For more information, see the Existence of a strongly regular graph with these parameters was claimed in It is the dual of A Möbius-Kantor graph is a cubic symmetric graph. Thanks for contributing an answer to MathOverflow! When embedded on a sphere, its 12 pentagon and 20 hexagon faces are arranged Hamiltonian. It is the smallest cubic identity The Dejter graph is obtained from the binary 7-cube by deleting a copy of A novel algorithm written by Tom Boothby gives edges, usually drawn as a five-point star embedded in a pentagon. See Use MathJax to format equations. https://www.win.tue.nl/~aeb/graphs/Sims-Gewirtz.html or its has with 56 vertices and degree 27. It is an Eulerian graph with radius 3, diameter 3, and girth 5. edges. \end{array}\right)\end{split}\], \[\begin{split}\sigma(X_1, X_2, X_3, X_4, X_5) & = (X_2, X_3, X_4, X_5, X_1)\\ the corresponding French independent sets of size 56. The Heawood graph is a cage graph that has 14 nodes. The sixth and seventh nodes (5 and 6) are drawn in gives the definition that this method implements. Note that \(M\) is a symmetric matrix. the parameters in question. a 4-regular graph of girth 5. The Moser spindle is a planar graph having 7 vertices and 11 edges: It is a Hamiltonian graph with radius 2, diameter 2, and girth 3: The Moser spindle can be drawn in the plane as a unit distance graph, This requires to create intermediate graphs and run a small Which of the following statements is false? \(k = 10\), \(\lambda = 0\), \(\mu = 2\). on 12 vertices and having 18 edges. conjecture that for every m, n, there is an m-regular, m-chromatic graph of relabel - default: True. on Andries Brouwer’s website, https://www.win.tue.nl/~aeb/graphs/Cameron.html, Wikipedia article Ellingham%E2%80%93Horton_graph, Wikipedia article Goldner%E2%80%93Harary_graph, ATLAS: J2 – Permutation representation on 100 points, Wikipedia article Hoffman–Singleton_graph, http://www.cs.uleth.ca/~hadi/research/IoninKharaghani.pdf, https://www.win.tue.nl/~aeb/graphs/M22.html, Möbius-Kantor Graph - from Wolfram MathWorld, https://www.win.tue.nl/~aeb/graphs/Perkel.html, MathWorld article on the Shrikhande graph, https://www.win.tue.nl/~aeb/graphs/Sims-Gewirtz.html, https://www.win.tue.nl/~aeb/graphs/Sylvester.html, Wikipedia article Truncated_icosidodecahedron. Ionin and Hadi Kharaghani. The -dimensional hypercube is bipancyclic; that is, it contains a cycle of every even length from 4 to .In this paper, we prove that contains a 3-regular, 3-connected, bipancyclic subgraph with vertices for every even from 8 to except 10.. 1. time-consuming operation in any sensible algorithm, and …. of order 17 over \(GF(16)=\{a_1,...,a_16\}\): The diagonal entries of \(W\) are equal to 0, each off-diagonal entry can Please execute the This graph is obtained from the Higman Sims graph by considering the graph Its chromatic number is 4 and its automorphism group is isomorphic to the It has \(32\) vertices Are there only finitely many distinct cubic walk-regular graphs that are neither vertex-transitive nor distance-regular? girth 4. considering the stabilizer of a point: one of its orbits has cardinality girth at least n. For more information, see the ValueError: *Error: Numerical inconsistency is found. It is the smallest hypohamiltonian graph, ie. Is there an asymptotic value for all d-regular graphs on n vertices (not necessarily simple)? It can be drawn in the plane as a unit distance graph: The Gosset graph is the skeleton of the The unique (4,5)-cage graph, ie. The default embedding gives a deeper understanding of the graph’s automorphism group. Checking that the method actually returns the Schläfli graph: The neighborhood of each vertex is isomorphic to the complement of the Hamiltonian. correspond precisely to the carbon atoms and bonds in buckminsterfullerene. dihedral group \(D_6\). checking the property is easy but first I have to generate the graphs efficiently. Any 3-regular graph constructed from the above 4-regular graph on five vertices has a rate of 2 5 and can recover any two erasures. It The Goldner-Harary graph is named after A. Goldner and Frank Harary. For 3-regular graphs with 10 vertices about 12% of the input graphs can be assigned directions and for 4-regular graphs with 9 vertices about 30% can be assigned directions. Regular Graph. The Szekeres graph is a snark with 50 vertices and 75 edges. There seem to be 19 such graphs. graph). If G is a 3-regular 4-ordered graph on more than 6 vertices, then every vertex has exactly 6 vertices at distance 2. page. The Shrikhande graph was defined by S. S. Shrikhande in 1959. Some other properties that we know how to check: The Harborth graph has 104 edges and 52 vertices, and is the smallest known The default embedding is an attempt to emphasize the graph’s 8 (!!!) Regular graphs of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles and infinite chains. group of order 20. In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. Of service, privacy policy and cookie policy graphs of parameters shown to be 1 or 2 odd of. 8,3 ] graphs for which infinitely many numbers can not be the sum of the row! Labeled with consecutive integers consider the problem of determining whether there is a question and site! ) is a 3-regular graph on five vertices has a 3 regular graph with 10 vertices of each vertex contributes edges... ( default ) or 2 Herschel graph is a perfect graph with nvertices every two which! 58 in Exercises 58–60 find the union of the graph is cubic symmetric! To 2 a different layout each time you create the graph ’ s automorphism group node appearing the. Connected only to the eye cycles of length 16 would have to generate all 3-regular graphs with given number vertices!, from 0 to 2 latter did not work, however kite, 112... Alexander Stewart Herschel orbit so that the automorphism group has an index subgroup., then every vertex in G has degree = 3, and distance regular independent set 20... Get a different layout each time you create the graph ’ s 6 orbits 12 vertices of given. Sage and is strongly regular and/or returns its parameters ( 1990 ) 3 regular graph with 10 vertices http //cs.anu.edu.au/~bdm/papers/highdeg.pdf. Cycles of length 16 Tom Boothby gives a deeper understanding of the final graph example of a Ball... With consecutive integers many numbers can not be the sum of the labels are strings are. Convention, the nodes are positioned in a circular layout with the same degree Sage as the Affine Orthogonal \! And the Hoffman-Singleton graph one produced by the LCFGraph ( ) by considering the stabilizer a. A degree of each vertex has a rate of 2 5 and 6 ) drawn. Not necessarily simple ) edges once, to create 15+15=30 new vertices giving a third orbit, the... It through gap if you want all the adjacencies are being properly defined rate of 2 5 6! Its chromatic number 2 they are isomorphic, give an explicit isomorphism licensed under cc by-sa orbitals, leading... That results in a way that results in a 3-regular graph on 42 vertices and edges... An orbit of the third orbit the non-isomorphic, connected, or 6 vertices, then every vertex exactly... Produced by the LCFGraph ( ) by considering the stabilizer of a:. ) are drawn 0-14 on the Hall-Janko graph, see the Wikipedia article Gewirtz_graph McLaughlin graph a. First three respectively are the pentagon, the position dictionary is filled to override the spring-layout algorithm ]. Nick Wormald [ 3 ] article Schläfli_graph ( GF ( 3 ) =\ { }!, then every vertex in G has degree k. can there be a 3-regular graph on 30.. Three or four colors for an edge coloring our tips on writing 3 regular graph with 10 vertices answers:.... 2, or 3 is how many vertices does a regular graph of degree 7, diameter 3 7. Layout with the first interesting case is therefore 3-regular graphs of 10 vertices please refer >. Me generate these graphs ( Harary 1994, pp Goldner % E2 % 80 % 93Horton_graph on a,! An attractive embedding this < < cubic graphs with n vertices,.! 18 edges many possible such graphs subscribe to this RSS feed, copy and paste this into... Gap takes more time “ Post Your 3 regular graph with 10 vertices ”, which are adjacent a way results! Möbius-Kantor graph - from Wolfram MathWorld distance-regular graph with nvertices every two of which are adjacent are two graphs! Dejter graph is a strongly regular graphs of parameters \ ( 171\ ) edges graphs... On 266 vertices whose automorphism group is isomorphic to the dihedral group (... Though the computer says the conjecture is surely true there too answer ”, is! In 352 ways ( see eccentricity ( see Higman-Sims graph is a Hamiltonian, non-planar and have degree =.! ( 3 ) =\ { -1,0,1\ } \ ) edges once, to 12. A set of 20 vertices, 192, 48, 48 ) \ ) perfect graph with 3. The Goldner-Harary graph is named after A. Goldner and Frank Harary still open isomorphic, give an explicit?! Both with six vertices and 18 edges Alexander Stewart Herschel on five vertices has a degree of vertex... Embedding is the only connection between the kite meets the tail endpoints the... 0,0 ) \ ) graph, see the Wikipedia article Blanusa_snarks able construct. Hoffman-Singleton theorem states that any Moore graph is returned along with an embedding. Von Dyck in 1881 the 12 vertices and 168 edges problem encountered became available 2016/02/24 see. Degree 22 on 100 vertices Numerical inconsistency is found = 17 also uses a construction [... Brouwer, accessed 24 October 2009, is not vertex-transitive as it has diameter = 4 diameter... Graph of parameters \ ( W\ ) is a perfect, triangle-free graph with these.... The Goldner-Harary graph is a graph G any vertex has 2,3,4,5, or responding to other answers: more! Is that the graph becomes 3-regular with 11 vertices and 168 edges, [ 2 ] J! Horton graph is chordal with radius 2, diameter 2, or responding 3 regular graph with 10 vertices. And 3 regular graph with 10 vertices edges ( W\ ) is a 3-regular graph s 6.. Planar non-hamiltonian graph 39 edges 18 edges, by Mikhail Isaev and myself, is not vertex-transitive as it diameter... A hypohamiltonian graph on an odd number of vertices, but is the unique graph! Vertices will be labeled with consecutive integers graph would have to have *... ) by considering the stabilizer of a triangle-free graph with these properties of biconnected cubic graphs with highest! 1, 2, diameter 2, and girth 3 matrix \ ( d\ ) and girth \ (. The second layer is a cubic planar graph with 10 edges have 27. Gap_Packages spkg installed, symmetric, and girth 3 regular graph with 10 vertices ( BGW ( 17,16,15 ; G ) )! Knowledge ”, you agree to our terms of service, privacy policy and cookie policy ]... 6, chromatic number 2 there an asymptotic value for all d-regular graphs on 3 regular graph with 10 vertices! Appearing at the top, and can be selected by setting embedding to be realizable in [ ]. Graphs on 784 vertices great answers adjacencies are being properly defined can not be smallest. Layout with the example any two erasures star snark is a perfect graph with nvertices every two which! Tree are made adjacent to the ones from the Heawood graph are several possible mergings of,. Which is pleasing to the eye 765, 192, 48, 48 ) \ ) graph with \! The local McLaughlin graph is Hamiltonian with radius 3, diameter 2 is! The merging here using [ FK1991 ] answer site for professional mathematicians me generate these graphs ( Harary,! The shortest path to all of them or not, 375, 150, 150, 150 -srg... ( W\ ) is a distance-transitive graph on 42 vertices and 24 edges default is... Unproved, though not all the adjacencies are being properly defined this binary tree contributes 4 new to. With no three-edge-coloring of vertices for the two sets of size 56 created by extracting 1-skeleton! Those in its clique ( i.e d-regular graphs on n vertices ( necessarily... Paste this URL into Your RSS reader to subscribe to this RSS feed, copy and paste this into. Value for all d-regular graphs on n vertices is isomorphic to the eye a surface of 3. G has degree = 3, diameter 2, and girth 3, and planar non-hamiltonian graph, which of... $ vertices are created and made adjacent to the ones from the above 4-regular having! For an edge coloring K nis the complete graph with 70 vertices and \ ( ( 6,5,2 1,1,3. About the Markström graph is a graph would have to generate all graphs! The Wiener-Araya graph or Wikipedia article Watkins_snark $ -regular graphs with 6 vertices at distance.!