On Some Classes of Equitable Irregular Graphs

Abstract

AbstractGraph labeling techniques are used by data scientists to represent data points and their relationships with each other. The segregation/sorting of similar datasets/points are easily done using labeling of vertices or edges in a graph. An equitable irregular edge labeling is a function \(f: E(G) \rightarrow N\) (not necessarily be injective) such that the vertex sums of any two adjacent vertices of \(G\) differ by at most one, where vertex sum of a vertex is the sum of the labels under \(f\) of the edges incident with that vertex. A graph admitting an equitable irregular edge labeling is called an equitable irregular graph (EIG). In this paper, more classes of equitable irregular graphs are presented. We further generalize the concept of equitable irregular edge labeling to \(k\)-equitable irregular edge labeling by demanding the difference of the vertex sum of adjacent vertices to be \(k \ge 1\).KeywordsEdge labelingDatasetsEquitable irregular graphk-equitable irregular edge labeling