Abstract

Let G = ( V ( G ), E ( G )) be a graph with the nonempty vertex set V ( G ) and the edge set E ( G ) . Let Z n be the group of integers modulo n and let k be a positive integer. A modular irregular labeling of a graph G of order n is an edge k -labeling Ļ† : E ( G )ā†’{1, 2, ā€¦, k } , such that the induced weight function Ļƒ : V ( G )ā†’ Z n defined by Ļƒ(v) = Ī£ ( uāˆˆN(v)) Ļ†(uv) (mod n) for every vertex v āˆˆ V ( G ) is bijective. The minimum number k such that a graph G has a modular irregular k -labeling is called the modular irregularity strength of a graph G , denoted by m s ( G ) . In this paper, we determine the exact values of the modular irregularity strength of some families of flower graphs, namely rose graphs, daisy graphs and sunflower graphs.

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