Proximity equitability colouring in graphs
Abstract
Let $G$ be a simple, finite, undirected and connected graph. Let S be the set of all vertices of maximum degree in $G$. The proximity of a vertex $u \in V(G)$ is the shortest distance of $u$ from $S$. Two vertices of $G$ are said to be proximity equitable if their proximity difference is at most 1. In this paper, a study of proximity equitable proper colouring is initiated.
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