written 4.9 years ago by
teamques10
★ 64k
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modified 23 months ago
by
pedsangini276
• 4.7k
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written 24 months ago by
sagarkolekar
★ 11k
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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.
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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