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arXiv · 1506.00813

On the Curling Number of Certain Graphs

Johan Kok·Naduvath Sudev·Chithra Sudev
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Abstract

In this paper, we introduce the concept of curling subsequence of simple, finite and connected graphs. A curling subsequence is a maximal subsequence $C$ of the degree sequence of a simple connected graph $G$ for which the curling number $cn(G)$ corresponds to the curling number of the degree sequence per se and hence we call it the curling number of the graph $G$. A maximal degree subsequence with equal entries is called an identity subsequence. The number of identity curling subsequences in a simple connected graph $G$ is denoted $ic(G).$ We show that the curling number conjecture holds for the degree sequence of a simple connected graph $G$ on $n \geq 1$ vertices. We also introduce the notion of the compound curling number of a simple connected graph $G$ and then initiate a study on the curling number of certain standard graphs like Jaco graphs and set-graphs.

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Johan Kok, Naduvath Sudev, Chithra Sudev. 2015-06-02. On the Curling Number of Certain Graphs. https://arxiv.org/abs/1506.00813

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