Edge irregular reflexive labeling of palm tree graph C3−B2,r and C3−B3,r
Rakel Junetty, Diari Indriati, Bowo Winarno · AIP conference proceedings · 2022
Let G be an undirected, connected, simple graph using vertex set V(G), also edge set E(G). The mapping of the elements of a graph to positive integers is called labeling a graph. An edge irregular reflexive k-labeling f is a labeling such that the label of edges are integers number {1, 2, 3, …, ke} and the label of vertices are even integers {0, 2, 4, …, 2kv}, k = max{ ke, 2kv}, so that the weight for all edges are not the same. In graph G, xy represents the edge, which means that the edge weight of xy is the total of edge label and vertices label attached to the edge. It is symbolized by wt(xy) is defined as wt(xy)=f(x)+f(xy)+f(y). We have the minimum k for where the graph G has an edge irregular reflexive k-labeling is known as reflexive edge strength, symbolized by (res(G)). This paper investigates the edge irregular reflexive labeling of palm tree graph Cp − Bq,r with p = 3, q = 2, 3 and r ≥ 3 and make sure the reflexive edge strength in both graphs.