Reflexive Edge Strength on Slanting Ladder Graph and Corona of Centipede and Null Graph
Mochamad Raffli Ispriyanto, Diari Indriati, Putranto Hadi Utomo · Indonesian Journal of Combinatorics · 2024
Assume G is a graph that is simple, undirected, and connected. If every edge label is a positive integer in the range 1 to ke, and every vertex label is a non-negative even number from 0 to 2kv, then a graph G is considered to have an edge irregular reflexive k-labeling, where k is defined as the maximum of ke and 2kv. The edge weight wt(ab) in the graph G, for the labeling λ, is defined as the function wt applied to the edge ab. The symbol res(G) denotes the reflexive edge strength, which is the largest label of the smallest k. The results of this research are as follows: res(SLm) for m≥2 is ⌈(3m−3)/3⌉ for 3m−3 ≢ 2, 3 (mod 6), and ⌈(3m−3)/3⌉+1 for 3m−3 ≡ 2, 3 (mod 6). res(Cpn ⊙ Nm) for n≥2, m≥1 is ⌈(2nm+2n−1)/3⌉ for 2nm+2n−1 ≢ 2, 3 (mod 6), and ⌈(2nm+2n−1)/3⌉+1 for 2nm+2n−1 ≡ 2, 3 (mod 6).