Reflexive edge strength of nonagon chain graph and triangle ribbon ladder graph

Abstract

Let G be an undirected, simple and connected graph with vertex set V (G) and egde set E(G). An edge irregular reflexive k-labeling f is labeling such that edges labeled with integers number 1, 2, ..., ke and vertices labeled with even integers 0, 2, ..., 2kv, where k = max{ke, 2kv} of a graph G such that the weights for all edge are distinct. The weight of edge xy in G, denoted by wt(xy) is defined as the sum of edge label and all vertices labels that are incident to that edge. The reflexive edge strength of a graph G which is denoted by res(G) is the minimum value k of the largest label on a graph G that can be labeled with edge irregular reflexive k-labeling. This article will review the k edge irregular reflexive labeling on the nonagon chain graph C(Nr) for r ≥ 2 and a triangular ribbon ladder graph LSPn for n ≥ 2 and determines the strength of the reflexive edges on the graph. The results of these graphs are res(C(Nr))= ⌈9r/3⌉, for 9r ̸≡ 2, 3 (mod 6), and ⌈9r/3⌉ + 1, for 9r ≡ 3 (mod 6). and res(LSPn)= ⌈6n−4/3⌉, for 6n − 4 ̸≡ 2, 3 (mod 6), and ⌈6n−4/3⌉ + 1, for 6n − 4 ≡ 2 (mod 6).