G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is              

Related MCQs

• Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?
• What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?
• Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.
• An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?
• The 2n vertices of a graph G corresponds to all subsets of a set of size n, for n>=4. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in G can be                        
• An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if
• Let G be an arbitrary graph with v nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie down between            and            
• If each and every vertex in G has degree at most 23 then G can have a vertex colouring of                      
• If each and every vertex in G has degree at most 23 then G can have a vertex colouring of                      
• Any subset of edges that connects all the vertices and has minimum total weight, if all the edge weights of an undirected graph are positive is called