Edge Irregular Reflexive Labeling on Corona of Path and Other Graphs

Abstract

Let G(V, E) be an undirected and simple graph with vertex set V and edge set E Define a k -labeling f on G such that the element belong to E are labeled with integers {1,2,⋯,ke } and the element belong to V are labeled with even integers {0,2,⋯,2kv }, where k = max{ke ,2kv }. A k -labeling f is mentioned as an edge irregular reflexive k -labeling if distinct edges have distinct weight. The weight of edge xy is denoted by wt(xy) and defined as wt(xy) = f (x) + f (xy) + f (y). A minimum k for which G has an edge irregular reflexive k -labeling is called reflexive edge strength of G and denoted by res(G). This paper contains investigation of edge irregular reflexive k -labeling for corona of path and other graphs and determination of their reflexive edge strengths.