Modular irregularity strength on some flower graphs

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 φ : E ( G )→{1, 2, …, k } , such that the induced weight function σ : V ( G )→ Z n defined by σ(v) = Σ ( u∈N(v)) φ(uv) (mod n) for every vertex v ∈ 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.