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All Journal Indonesian Journal of Combinatorics
Ispriyanto, Mochamad Raffli
Sebelas Maret University
Computer Science & IT Decision Sciences, Operations Research & Management

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Reflexive Edge Strength on Slanting Ladder Graph and Corona of Centipede and Null Graph Ispriyanto, Mochamad Raffli; Indriati, Diari; Utomo, Putranto Hadi
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.3

Abstract

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).
Co-Authors Diari Indriati Putranto Hadi Utomo