A generic algorithm or method to solve this question is 1: procedure isV alidDegreeSequence(L) 2: for n in list L do 3: if L doesn’t have n elements next to the current one then return false 4: decrement next n elements of the list by 1 5: arrange it back as a degree sequence, i.e. Which of the following statements for a simple graph is correct? View Answer, 13. d) 16 So, graph K5 has minimum vertices and maximum edges than K3,3. 1. there is a path of length ≤ 2 from u and v in E, Where V4 is the set of vertics in G which are not isolated, If we reverse directions of all arcs in a graph, the new graph has same set of strongly connected components as the original graph. Hence tuple <3, 3, 3, 1, 0, 0> is not graphic. . This Test Section specifically contain the hand picked Multiple choice Questions and Answers asked in the various competitive exam.this section mainly contain the MCQ on Data Structure and Algorithms - Graph. The answer is, ξ(G) and ξ(T) is same for two trees, then the trees have same number of vertices. Try this amazing The Cardiac Cycle Quiz Questions! View Answer, 8. Prerequisite – Graph Theory Basics – Set 1 A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense “related”. d) A graph may contain no vertices and many edges c) Adjacency List, Adjacency Matrix as well as Incidence Matrix There is always one unbounded face, so the number of bounded faces = 6, Which of the following graphs is isomorphic to, Let G be a complete undirected graph on 6 vertices. c) v + 1 = e dn with d1 ≥ d2 ≥ d2 ≥ . Now, we apply this theorem to given sequences: option I) 7,6,5,4,4,3,2,1 → 5,4,3,3,2,1,0 → 3,2,2,1,0,0 → 1,1,0,0,0 → 0,0,0,0 so its graphical. f = 7 A) FALSE: A disconnected graph can be planar as it can be drawn on a plane without crossing edges. a) 15 The expression ξ(G) is basically sum of all degrees in a tree. a) B and E A cycle on n vertices is isomorphic to its complement. Below is a cyclic graph with 5 vertices and its complement graph. . . d) Complete Graph Option IV) 8,7,7,6,4,2,1,1 , here degree of a vertex is 8 and total number of vertices are 8 , so it’s impossible, hence it’s not graphical. The resultant graph is two edge connected, and of minimum degree 2 but there exist a cut vertex, the merged vertex. Let it be true for n vertices. d) Information given is insufficient Therefore, degree of all vertices should be be from 1 to n-1. c) A and E Now E and F should not be connected to any vertex in the graph. = 800 + 106 + 106 b) Regular Graph A) Any k-regular graph where k is an even number. For every subset of k vertices, the induced subgraph has at most 2k-2 edges, The minimum cut in G has at least two edges, There are two edge-disjoint paths between every pair to vertices, There are two vertex-disjoint paths between every pair of vertices. a) uvnwxny b) uvnwnxny c) uv2nwx2ny d) All of the mentioned 2. Note − Let ‘G’ be a connected graph with ‘n’ vertices, then. is not Eulerian as a k regular graph may not be connected (property b is true, but a may not) B) A complete graph on 90 vertices is not Eulerian because all vertices have degree as 89 (property b is false) C) The complement of a cycle on 25 vertices is Eulerian. Which of the following properties does a simple graph not hold? (Q) The line graph of a clique is a clique. d) (n*n-n+2*m)/2 Now to fulfill the requirement of A, B and C, the node D will never be able to get its degree as 1. II. Join our social networks below and stay updated with latest contests, videos, internships and jobs! There is an edge between (a, b) and (c, d) if |a − c| <= 1 and |b − d| <= 1. There can be total 6C4 ways to pick 4 vertices from 6. in descending order 6: if any element of the list becomes negative then return false 7: return true Rationale behind this method comes from the properties of simple graph. Which of the following is/are not an application of turing machine? f is number of faces including bounded and unbounded, 10 - 15 + f = 2 a) True What is the maximum number of edges in a bipartite graph having 10 vertices? If a simple graph G, contains n vertices and m edges, the number of edges in the Graph G'(Complement of G) is ___________ a) Every path is a trail (S) The line graph of a tree is a tree. 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