Some New Results on the Curling Number of Graphs

N. K. Sudev; C. Susanth; K. P. Chithra; Johan Kok; Sunny Joseph Kalayathankal

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arXiv · 1510.01271

Some New Results on the Curling Number of Graphs

N. K. Sudev·C. Susanth·K. P. Chithra·Johan Kok·Sunny Joseph Kalayathankal

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Abstract

Let $S=S_1S_2S_3\ldots S_n$ be a finite string. Write $S$ in the form $XYY\ldots Y=XY^k$, 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, $X^{k_1}_1\circ X^{k_2}_2\circ X^{k_3}_3 \ldots \circ X^{k_l}_l$. The compound curling number of $G$, denoted $cn^c(G)$ is defined to be, $cn^n(G) = \prod\limits^{l}_{i=1}k_i$. In this paper, we discuss the curling number and compound curling number of certain products of graphs.

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BibTeX RIS

N. K. Sudev, C. Susanth, K. P. Chithra, Johan Kok, Sunny Joseph Kalayathankal. 2015-10-01. Some New Results on the Curling Number of Graphs. https://arxiv.org/abs/1510.01271

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