On Chromatic Curling Number of Graphs

TL;DR

This paper introduces the concept of chromatic curling number, combining graph coloring with the curling number of degree sequences, and studies its properties for specific graphs.

Contribution

It defines the chromatic curling number based on minimum parameter colorings and analyzes its characteristics for certain classes of graphs.

Findings

Defined the chromatic curling number for graphs.

Analyzed properties for specific graph classes.

Connected coloring parameters with degree sequence repetitions.

Abstract

The curling number of a graph G is defined as the number of times an element in the degree sequence of G appears the maximum. Graph colouring is an assignment of colours, labels or weights to the vertices or edges of a graph. A colouring $\mathcal{C}$ of colours $c_1,c_2,\ldots,c_l$ is said to be a minimum parameter colouring if C consists of a minimum number of colours with smallest subscripts. In this paper, we study colouring version of curling number of certain graphs, with respect to their minimum parameter colourings.