11 research outputs found
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
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 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
Chromaticity of a family of K4-homeomorphs
AbstractWe discuss the chromaticity of one family of K4-homeomorphs which has exactly 2 adjacent paths of length 1, and give sufficient and necessary condition for the graphs in the family to be chromatically unique