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

An L(2,1)-labelling of a graph $G=(V, E)$ is $λ_{2,1}(G)$ 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 $λ_{2,1}(G)$ 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 $λ_{2,1}(G)$ is $Δ+3ω$, where $Δ$ and $ω$ represents the maximum degree of the vertices and size of maximum clique respectively.