Discrete Mathematics

Graph G1 (v1, e1) and G2 (v2, e2) are said to be an isomorphic graphs if there exist a one to one correspondence between their vertices and edges. In other words, both the graphs have equal number of vertices and edges. May be the vertices are different at levels.

ISOMORPHIC GRAPHS (1)

ISOMORPHIC GRAPHS (2)

These pictures below are graphed as letters. Find all the isomorphic graphs from these letters.

Solution: The Isomorphic graphs are Word

• A and R
• F and T
• S and K
• Z, M, V and S

Key Note: Isomorphic Graphs must have equal number of vertices with same degree and equal number of vertices and edges.
Homeomorphic Graphs
In a Graph G, if another graph G* can be obtained by dividing edge of G with additional vertices or we can say that a Graph G* can be obtained by introducing vertices of degree 2 in any edge of a Graph G, then both the graph G and G* are known as Homeomorphic graphs.

The graph B and C are not the isomorphic graph, since they are obtained by the graph A, they are homeomorphic graphs. Same as D is the isomorphic graph.
Important Point to remember: Homeomorphic graphs have same degree of each vertex, which is inserted in the graphs