On the Modular Irregularity Strength of Some Graph

Abstract

Let G be a simple graph of order n, with no component of order two. Define an edge l-labeling θ:E(G)→{1,2,…,1}. Let xϵV(G), the weight of x is the sum of the l-labels of all its incident edges, denoted by α(x)=Σ░⟦θ(xy)⟧. The edge l-labeling is said modular irregular l-labeling of G if there exists a bijective weight α-function from V(G) to the group of integers modulo n. The smallest positive integer l such that G has a modular irregular l-labeling is said the modular irregularity strength of G, denoted by ms(G). Write ms(G)=∞, if G has no modular irregular strength. In this paper, we find ms of some graph classes, i.e. sunlet graphs, cycle barbell graphs, and m-Harary cycle graphs.

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