Chromatic Completion Number

TL;DR

This paper introduces the chromatic completion number, a new graph parameter based on proper vertex coloring, and computes it for specific classes of graphs, opening avenues for further research.

Contribution

It defines the chromatic completion number and determines its value for cycle derivative graphs and helm graphs, expanding understanding of graph coloring properties.

Findings

Chromatic completion number is introduced as a new graph parameter.

Exact values are computed for cycle derivative graphs and helm graphs.

The paper suggests directions for future research in graph coloring.

Abstract

We use a well known concept of proper vertex colouring of a graph to introduce the construction of a chromatic completion graph and its related parameter, the chromatic completion number of a graph. We then give the chromatic completion number of certain classes of cycle derivative graphs and helm graphs. Finally, we discuss further problems for research related to this concept.