Complementary Eccentric Uniform Labeling Graphs

Abstract

Given a graph \(G=(V,E)\), a set \(M\subset V\) is called Complementary Eccentric Uniform (CEU), if the \(M\)-eccentricity labeling \(e_M(u)=\max\{d(u,v):v\in M\}\) is identical for all \(u\in V-M\). The least cardinality of a CEU set is called the CEU number of the graph \(G\). In this paper we initiate a study on CEU labelled graphs and obtain bounds for certain graphs.