Cutpoints and the chromatic polynomial | Zendy

Whitehead Earl Glen | Zendy; Zhao LianChang | Zendy

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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.

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