Some New Results on the Curling Number of Graphs

Abstract

Let $S=S_1{S}_2{S}_3\dots S_n$ be a finite string. Write $S$ in the form $XYY\dots Y=X{Y}^k$, consisting of a prefix $X$ (which may be empty), followed by $k$ copies of a non-empty string $Y$. Then, the greatest value of this integer $k$ is called the curling number of $S$ and is denoted by $cn(S)$. Let the degree sequence of the graph $G$ be written as a string of identity curling subsequences say, $X_1^{k_1}\circ X_2^{k_2}\circ X_3^{k_3}\dots \circ X_l^{k_l}$. The compound curling number of $G$, denoted $c{n}^c(G)$ is defined to be, $c{n}^n(G)=\prod _{i=1}^l{k}_i$. In this paper, we discuss the curling number and compound curling number of certain products of graphs.

11 Pages in Journal of Combinatorial Mathematics and Combinatorial Computing, 2016

References in corpus (2)

• On Integer Additive Set-Indexers of Graphs
• Curling Numbers of Certain Graph Powers

Cited by in corpus (2)

• On Chromatic Curling Number of Graphs
• A study on the curling number of graph classes