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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.
written 5.6 years ago by gravatar for teamques10 teamques10 ★ 68k modified 2.6 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k
discrete mathematics
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written 2.7 years ago by gravatar for sagarkolekar sagarkolekar ★ 11k

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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