Edge irregular reflexive labeling on double broom graph and comb of cycle and star graph

Abstract

Assume that G is a connected, undirected, simple graph with V (G) as its vertex set and E(G) as its edge set. A labeling technique known as edge irregular reflexive labeling allows each vertex to have a label that is a non-negative even number from 0 to 2kv, and each edge to have a label that is a positive integer from 1 to ke, with distinct weights for each edge. The smallest k of the largest label in graph G, represented by res(G), is the reflexive edge strength. The paper’s contents determine the reflexive edge strength of double broom graph B(r, s, s) with r, s ≥ 2, and comb of cycle and star graph Cr ▷ Ss with r ≥ 3, s ≡ 2, 5 (mod 6).