Edge irregular reflexive labeling on umbrella graphs U_(3,n) and U_(4,n)

摘要

Let G be an undirected and connected graph with vertex set V(G) and edge set E(G). An edge irregular reflexive k-labeling is a function f_e : E(G) → {1, 2,..., k_e} and a function f_v : V(G) → {0,2,...,2k_v}, where k = max {k_e, 2k_v} of a graph G such that the weights for all edge is distinct. Under f labeling for edges and vertices, the weight of edge xy in G, denoted by wt(xy) is defined as wt(xy) = f(x) + f(xy) + f(y). The minimum k for which the graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength, denoted by res(G). This paper contains investigation of edge irregular reflexive k-labeling of umbrella graphs U_(3,n) and U_(4,n).