Issue |
ITM Web Conf.
Volume 61, 2024
The 9th International Symposium on Current Progress in Mathematics and Sciences 2023 (The 9th ISCPMS 2023) in conjunction with AUA Academic Conference on the Application of Artificial Intelligences and Data Sciences in a Modern Science for a Better Life
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Article Number | 01001 | |
Number of page(s) | 10 | |
DOI | https://doi.org/10.1051/itmconf/20246101001 | |
Published online | 10 January 2024 |
Modular irregularity strength of disjoint union of cycle-related graph
Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok 16424, Indonesia
* Corresponding author: kiki@sci.ui.ac.id
Let G = (V,E) be a graph with a vertex set V and an edge set E of G, with order n. Modular irregular labeling of a graph G is an edge k-labeling φ:E → {1, 2,…,k} such that the modular weight of all vertices is all different. The modular weight is defined by wtφ(u) = Σv∈N(u) φ(uv) (mod n). The minimum number k such that a graph G has modular irregular labeling with the largest label k is called modular irregularity strength of G. In this research, we determine the modular irregularity strength for a disjoint union of cycle graph, for n ≡ 0 (mod 4), a disjoint union of sun graph, ms(m(Cn ⊙ K1))2 = ∞ for n and m even and ms(m(Cn ⊙ K1)) = mn otherwise, and a disjoint union of middle graph of cycle graph, ms(mM(Cn)) = ∞ for n and m both odd numbers and otherwise.
Key words: Modular irregularity strength / disjoint union of graph / cycle graph / sun graph / middle graph of cycle graph
© The Authors, published by EDP Sciences, 2024
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