Graph isomorphism is concerned with:A. The number of vertices and edgesB. The degrees of verticesC. The labeling of vertices and edgesD. The structural equivalence of graphs
Question
Graph isomorphism is concerned with:A. The number of vertices and edgesB. The degrees of verticesC. The labeling of vertices and edgesD. The structural equivalence of graphs
Solution
The correct answer is D. Graph isomorphism is concerned with the structural equivalence of graphs. This means that two graphs are isomorphic if there is a one-to-one correspondence between their vertices and edges that preserves the connectivity of the graphs. The number of vertices and edges, the degrees of vertices, and the labeling of vertices and edges can all be different between two isomorphic graphs.
Similar Questions
Which of the following statements is not true for isomorphic graphs?a.Number of vertices in both the graphs must be same.b.Number of edges in both the graphs must be same.c.They have n+1 connected componentsd.Degree sequence of both the graphs must be same.
A graph can be defined as a collection of:a.Verticesb.Edgesc.Both vertices and edgesd.None of the above
The subgraph-isomorphism problem takes two undirected graphs G1 and G2, andit asks whether G1 is isomorphic to a subgraph of G2. Show that the subgraph-isomorphism problem is NP-complete.
or each of the classes Ci below determine the smallest n for which Cicontains nonisomorphic n-vertex graphs with the same degree sequence:(a) C1 = { all graphs }, (b) C2 = { loopless graphs }, (c) C3 = { simplegraphs }
What is the degree of a vertex in a graph?a) Number of edges connected to the vertexb) Number of vertices in the graphc) Number of self-loopsd) Number of paths through the vertex
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.