Chromatic uniqueness of a family of K4-homeomorphs

AbstractWe discuss the chromaticity of one family of K4-homeomorphs which has girth 7, and give sufficient and necessary condition for the graphs in the family to be chromatically unique

Chromaticity of a family of K4 homeomorphs

AbstractA K4 homeomorph can be described as a graph on n vertices having 4 vertices of degree 3 and n − 4 vertices of degree 2; each pair of degree 3 vertices is joined by a path. We study the chromatic uniqueness and chromatic equivalence of one family of K4 homeomorphs. This family has exactly 3 paths of length one. The results of this study leads us to solve 3 of the problems posed by Koh and Teo in their 1990 survey paper which appeared in Graphs and Combinatorics

Chromaticity Of Certain K4-Homeomorphs

The chromaticity of graphs is the term used referring to the question of chromatic equivalence and chromatic uniqueness of graphs. Since the arousal of the interest on the chromatically equivalent and chromatically unique graphs, various concepts and results under the said areas of research have been discovered and many families of such graphs have been obtained. The purpose of this thesis is to contribute new results on the chromatic equivalence and chromatic uniqueness of graphs, specifically, K4-homeomorphs

Graphs determined by polynomial invariants

AbstractMany polynomials have been defined associated to graphs, like the characteristic, matchings, chromatic and Tutte polynomials. Besides their intrinsic interest, they encode useful combinatorial information about the given graph. It is natural then to ask to what extent any of these polynomials determines a graph and, in particular, whether one can find graphs that can be uniquely determined by a given polynomial. In this paper we survey known results in this area and, at the same time, we present some new results

On chromatic equivalence of a pair of K4-homeomorphs

Let P(G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically euqivalent, denoted G ∼ H, if P(G, λ) = P(H, λ). We write [G] = {H/H ∼ 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 K4-homeomorphs, K4(1, 2, 8, d, e, f). The obtained result can be extended in the study of chromatic equivalence classes of K4(1, 2, 8, d, e, f) and chromatic uniqueness of K4-homeomorphs with girth 11