Chromatic equivalence and uniqueness of certain (n,n+2)-graphs
Qiuhong Deng · Journal of Dalian Maritime University · 2004
The length of a shortest cycle of a graph G is called the girth of G. Two graphs are said to be chromatically equivalent if they have the same chromatic polynomial. A graph G is said to be chromatically unique if for any graph H which is chromatically equivalent to G implies that H isomorphic to G. Finding chromatically unique graphs is an interesting problem in graph theory. The chromaticity of 2-connected (n,n+2) graphs which contain a 4-cycle or two triangles, or which have girth 5 and are not homeomorphic to K_4 had been discussed. In this paper, based on the homeomorphic classification and comparing the coefficients of the chromatic polynomials of the family of 2-connected (n,n+2) graphs that have girth 6 and are not homeomorphic to K_4, the chromatically equivalent subfamilies and the chromatically unique subfamilies of the family are presented.