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arXiv · 1407.5488

L(2,1)-labelling of Circular-arc Graph

Satyabrata Paul·Madhumangal Pal·Anita Pal
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Abstract

An L(2,1)-labelling of a graph $G=(V, E)$ is $\lambda_{2,1}(G)$ a function $f$ from the vertex set V (G) to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The L(2,1)-labelling number denoted by $\lambda_{2,1}(G)$ of $G$ is the minimum range of labels over all such labelling. In this article, it is shown that, for a circular-arc graph $G$, the upper bound of $\lambda_{2,1}(G)$ is $\Delta+3\omega$, where $\Delta$ and $\omega$ represents the maximum degree of the vertices and size of maximum clique respectively.

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Satyabrata Paul, Madhumangal Pal, Anita Pal. 2014-07-21. L(2,1)-labelling of Circular-arc Graph. https://arxiv.org/abs/1407.5488

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