The Modular Irregularity Strength of C_n⊙mK_1

Abstract

Let G(V, E) be a graph with order n with no component of order 2. An edge k-labeling α: E(G) →{1,2,…,k} is called a modular irregular k-labeling of graph G if the corresponding modular weight function wt_ α:V(G) → Z_n defined by wt_ α(x) =Ʃ_(xyϵE(G)) α(xy) is bijective. The value wt_α(x) is called the modular weight of vertex x. Minimum k such that G has a modular irregular k-labeling is called the modular irregularity strength of graph G. In this paper, we define a modular irregular labeling on C_n⊙mK_1. Furthermore, we determine the modular irregularity strength of C_n⊙mK_1.Keywords: corona product; cycle; empty graph; modular irregular labeling; modular irregularity strength. AbstrakDiberikan graf G(V, E) dengan orde n dengan tidak ada komponen yang berorde 2. Sebuah pelabelan-k sisi α: E(G) →{1,2,…,k} disebut pelabelan-k tak teratur modular pada graf G jika fungsi bobot modularnya wt_ α:V(G) → Z_n dengan wt_ α(x) =Ʃ_(xyϵE(G)) α(xy) merupakan fungsi bijektif. Nilai wt_α(x) disebut bobot modular dari simpul x. Minimum dari k sehingga G mempunyai pelabelan-k tak teratur modular disebut dengan kekuatan ketakteraturan modular dari graf G. Pada tulisan ini, didefinisikan pelabelan tak teratur modular pada C_n⊙mK_1. Lebih lanjut, ditentukan kekuatan ketakteraturan modular dari C_n⊙mK_1.Kata Kunci: hasil kali korona; lingkaran, graf kosong; pelabelan tak teratur modular; kekuatan ketakteraturan modular.

Modular irregularity strength of disjoint union of cycle-related graph

“…Then Hinding et al determined the modular irregularity strength of the dodecahedralmodified generalization graph [9]. Dewi determined the modular irregularity strength of 𝐶𝐶 𝑛𝑛 ⊙ 𝑚𝑚𝐾𝐾 1 [10]. Recently, Sugeng determined the modular irregularity strength of 𝑚𝑚(𝐶𝐶 𝑛𝑛 ) and several other flower-type graphs [11].…”

“…The ms(𝐶𝐶 𝑛𝑛 ), ms(𝐶𝐶 𝑛𝑛 ⊙ 𝑚𝑚𝐾𝐾 1 ), and ms(𝑚𝑚(𝐶𝐶 𝑛𝑛 )) have been determined [3,10,11]. In this research, we determine the modular irregularity strength for a disjoint union of the cycle graph, a disjoint union of the sun graph, and a disjoint union of the middle graph of the cycle graph.…”