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Define isomorphism of graphs. find if the following two graphs are isomorphic. if yes find one to one correspondence between the vertices.
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Define isomorphism of graphs. find if the following two graphs are isomorphic. if yes find one to one correspondence between the vertices.

Solution:

Let $G_1$ and $G_2$ be the two given graph then they are said to be isomorphic to each other if following conditions are satisfied.

a) No. of vertices of $G_1$ = No of vertices of $G_2$

b) No of angles of $G_1$ = No of edges of $G_2$

c) Both the graph must have same number of vertices with equal degree.

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1] No. of vertices of $G_1$ = No of vertices of $G_2$

$V(G_1) = V(G_2)$

8 = 8

2] No of edges of $G_1$ = No of edges of $G_2$

$E(G_1) = E(G_2)$

12 = 12

3]

Definition of vertices of $G_1$ Definition of vertices of $G_2$
def(A) = 3 def (A) = 3
def(B) = 3 def(B) = 3
def (C) = 3 def (C) = 3
def (D) = 3 def (D) = 3
def (E) = 3 def (E) = 3
def (F) = 3 def (F) = 3
def (G) = 3 def (H) = 3
def(H) = 3 def (H) = 3

$\therefore$ Both the graph $G_1$ and $G_2$ isomorphic to each other.

One to one correspondence between $G_1$ and $G_2$

Graph $G_1$ A B C D E F G H
Graph $G_2$ A F D G E B C H
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