Super vertex mean labeling of cycles through different ways

Abstract

A super vertex mean labeling 𝑓 of a (p,q) - graph G = (V,E) is defined as an injection from E to the set {1,2,3,···,p+q} that induces for each vertex v the label defined by the rule , where Ev denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,···,p+q}. In this paper, we investigate the super vertex mean labeling behavior of cycles by giving various ways by which they can be labeled.