DEGREE SEQUENCE
The degree sequence of a graph is the sequence of the degrees of the vertices,
with these numbers put in ascending order, with repetitions as needed. Thus
G:
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has degree sequence
(1,2,2,3).
Two graphs with different degree sequences cannot be isomorphic. For example,
these two graphs are not isomorphic,
G1:
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G2:
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since one has four vertices of degree 2 and the other has just two. Their degree
sequences are
(2,2,2,2) and (1,2,2,3).
It is common for even simple connected graphs to have the same degree sequences
and yet be non-isomorphic. For example, we saw in class that these
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are not isomorphic, but they both have the degree sequence
(2,2,2,2,3,3,3,3).
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