Opuscula Math. 30, no. 2 (), 123-131
http://dx.doi.org/10.7494/OpMath.2010.30.2.123
Opuscula Mathematica

On chromatic equivalence of a pair of K4-homeomorphs

Abstract. Let $$P(G, \lambda)$$ be the chromatic polynomial of a graph $$G$$. Two graphs $$G$$ and $$H$$ are said to be chromatically equivalent, denoted $$G \sim H$$, if $$P(G, \lambda) = P(H, \lambda)$$. We write $$[G] = \{H| H \sim G\}$$. If $$[G] = \{G\}$$, then $$G$$ is said to be chromatically unique. In this paper, we discuss a chromatically equivalent pair of graphs in one family of $$K_4$$-homeomorphs, $$K_4(1, 2, 8, d, e, f)$$. The obtained result can be extended in the study of chromatic equivalence classes of $$K_4(1, 2, 8, d, e, f)$$ and chromatic uniqueness of $$K_4$$-homeomorphs with girth $$11$$.
Keywords: chromatic polynomial, chromatic equivalence, $$K_4$$-homeomorphs.
Mathematics Subject Classification: 05C15.