On chromatic D-polynomials of Mycielskian of paths and cycles

Abstract

Graph colouring is an assignment of colours, labels or weights to elements of a graph subject to certain constraints. Coloring the vertices of a graph in such a way that adjacent vertices are having different colours is called proper vertex colouring. A proper vertex colouring using minimum parameters of colours is studied extensively in recent literature. In this paper, we define new polynomials called chromatic D-polynomial and modified chromatic D-polynomial in terms of minimal parameter colouring and structural characteristics of graphs such as distances and degrees of vertices.