The reflexive edge strength on some almost regular graphs

A function f with domain and range are respectively the edge set of graph G and natural number up to [Formula: see text] , and a function f with domain and range are respectively the vertex set of graph G and the even natural number up to [Formula: see text] are called a total k-labeling where [Formula: see text]. The total k-labeling of graph G by the condition that every two different edges have different weight is called an edge irregular reflexive k-labeling, where for any edge [Formula: see text] , the weight is [Formula: see text]. The reflexive edge strength of the graph G, denoted by [Formula: see text] is the minimum k for graph G which has an edge irregular reflexive k-labelling. In this study, we obtained the [Formula: see text] of graphs which their vertex degrees show an almost regularity properties.