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Cutpoints and the chromatic polynomial
Author(s) -
Whitehead Earl Glen,
Zhao LianChang
Publication year - 1984
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190080305
Subject(s) - chromatic polynomial , mathematics , combinatorics , chromatic scale , friendship graph , windmill graph , multiplicity (mathematics) , foster graph , uniqueness , simple graph , graph , discrete mathematics , tutte polynomial , polynomial , voltage graph , line graph , mathematical analysis
We prove that the multiplicity of the root 1 in the chromatic polynomial of a simple graph G is equal to the number of nontrivial blocks in G . In particular, a connected simple graph G has a cutpoint if and only if its chromatic polynomial is divisible by (λ – 1) 2 . We apply this theorem to obtain some chromatic equivalence and uniqueness results.