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) = 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 ms(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.