Answer to Question #137179 in Discrete Mathematics for shanto

Question

Explain graph isomorphism with proper diagrams.

Answer 1

An isomorphism exists between two graphs G and H if:

1. Number of vertices of G = Number of vertices of H.

2. Number of edges of G = Number of edges of H.

Please note that the above two points do not guarantee isomorphism.

In addition, if f is a function obtained from a relationship between the vertices of G and the vertices of H, then f should be a one to one and onto function (bijection) and the number of vertices with same degree, must be same in G and H. A degree is the number of edges connected to a vertex.