The reflexive edge strength on some almost regular graphs

Abstract A function f with domain and range are respectively the edge set of graph G and natural number up to k e , and a function f with domain and range are respectively the vertex set of graph G and the even natural number up to 2 k v are called a total k-labeling where k = m a x \{ k e , 2 k v \} . 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 x 1 x 2 , the weight is w t \( x 1 x 2 \) = f v \( x 1 \) + f e \( x 1 x 2 \) + f v \( x 2 \) . The reflexive edge strength of the graph G, denoted by r e s \( G \) is the minimum k for graph G which has an edge irregular reflexive k-labelling. In this study, we obtained the r e s \( G \) of graphs which their vertex degrees show an almost regularity properties.