Edge irregular reflexive labeling on banana tree graphs B 2, nand B 3, n

Abstract

Let G be an undirected and simple graph with vertices set V(G) and edges set E(G). An edge irregular reflexive k-labeling f such that element edges labeled with integers number {1,2,?,ke} and vertices labeled with even integers {0,2,?,2kv}, k = max{ke, 2kv} of a graph G such that the weights for all edges are distinct. The weight of edge xy in G, symbolized by wt(xy) is defined as wt(xy) = f(x) + f(xy) + f(y). Reflexive edge strength is the minimum k for which the graph G has an edge irregular reflexive k-labeling, notated by res(G). In this paper we determine the exact values of the reflexive edge strength of banana tree graphs B2,n and B3,n.