Abstract
Let G= (V, E) be a graph order n and an edge labeling ψ: E→{1,2,…,k}. Edge k labeling ψ is to be modular irregular -k labeling if exist a bijective map σ: V→Zn with σ(x)= ∑yϵv ψ(xy)(mod n). The modular irregularity strength of G (ms(G))is a minimum positive integer k such that G have a modular irregular labeling. If the modular irregularity strength is none, then it is defined ms(G) = ∞. Investigating the firecrackers graph (Fn,2), we find irregularity strength of firecrackers graph s(Fn,2), which is also the lower bound for modular irregularity strength, and then we construct a modular irregular labeling and find modular irregularity strength of firecrackers graph ms(Fn,2). The result shows its irregularity strength and modular irregularity strength are equal.
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