For each pair of graphs G and G ′ in 1—5, determine whether G and G ′ are isomorphic. If they are, give functions g : V ( G ) → V ( G ′ ) and h : E ( G ) → E ( G ′ ) that define the isomorphism. If they are not, give an invariant for graph isomorphism that they do not share. 5.
For each pair of graphs G and G ′ in 1—5, determine whether G and G ′ are isomorphic. If they are, give functions g : V ( G ) → V ( G ′ ) and h : E ( G ) → E ( G ′ ) that define the isomorphism. If they are not, give an invariant for graph isomorphism that they do not share. 5.
Solution Summary: The author explains that the graphs are not isomorphic, because a vertex v 5 has degree 5 whereas no verticle in graph Gprime
For each pair of graphs G and
G
′
in 1—5, determine whether G and
G
′
are isomorphic. If they are, give functions
g
:
V
(
G
)
→
V
(
G
′
)
and
h
:
E
(
G
)
→
E
(
G
′
)
that define the isomorphism. If they are not, give an invariant for graph isomorphism that they do not share.
Determine whether the following graphs are isomorphic.
v2
V3
fi
u2
el
'n
Is
f3
e4
es
U4
f4
V4
Vs
5 f
fo
U3
G1
G?
b)
W6
X2
as
p6
a2
XI
X3
Ps
W4
pi
P2
X4
Ws
XS
H1
H2
(c) Prove that the two graphs below are isomorphic.
9.
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