A Study on the Curling Number of Certain Graph Classes

Abstract

Given a finite non-empty sequence $S$ of integers, write it as $X{Y}^k$, consisting of a prefix $X$ (which may be empty), followed by $k$ copies of a non-empty string $Y$. Then, the greatest such integer $k$ is called the curling number of $S$ and is denoted by $cn(S)$. The notion of curling number of graphs has been introduced in terms of their degree sequences, analogous to the curling number of integer sequences. In this paper, we study the curling number of certain graph classes and graphs associated to given graph classes.