Did you know? The study of these properties is part of the branch of Mathematics known as topology. Isomorphic graphs are topologically equivalent. You can show isomorphism by using a reasoned argument or by setting up a correspondence between the sets of vertices. WORKED EXAMPLE 1.24
PL E
Show that these graphs are isomorphic.
Straighten out edge W Z and relabel the vertices: W = A, X = B, Y = C , Z = D
Set up a correspondence between the sets of vertices.
M
WORKED EXAMPLE 1.25
SA
Show that these graphs are isomorphic.
Relabel
U = A, W = B, V = C , X = D, Y = E
and Z
Compare the vertex degrees to suggest a possible correspondence.
= F
Common error A necessary condition for two graphs to be isomorphic is that they have the same vertex degrees. However, this is not a sufficient condition, as two graphs can have the same degree but not be isomorphic.
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