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Graphs with Constant Modular Irregularity Strength | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 آبان 1405 اصل مقاله (492.5 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30751.2607 | ||
| نویسندگان | ||
| K.A. Sugeng* 1، 2؛ Z.Z. Barack1؛ M. Augurius1؛ L. Yehezkiel1؛ P. John1؛ A. Semaničová-Feňovčíková3؛ M. Bača3؛ L. Mella4 | ||
| 1Combinatorics and Algebra Research Group, Department of Mathematics, Faculty Mathematics and Natural Science, Universitas Indonesia, Depok, Indonesia | ||
| 2Center for Research Collaboration for Graph Theory and Combinatorics | ||
| 3Department of Applied Mathematics and Informatics, Technical University of Košice, Košice, Slovakia | ||
| 4Dip. di Scienze Fisiche, Informatiche, Matematiche, Universitá degli Studi di Modena e Reggio Emilia, Via Campi 213/A, I-41125 Modena, Italy | ||
| چکیده | ||
| We consider a finite, connected graph $G(V,E)$ of order $n$. An edge $k$-labeling $\phi : E \to \{1,2,\dots,k\}$ is called a modular irregular labeling of a graph $G$ if the weight function, $\sigma:V(G) \to \mathbb{Z}_n$, defined by $\sigma(u) = wt_\phi (u) = \sum_{uv \in E(G)}\phi(uv) \pmod{n}$ is bijective, where $\mathbb{Z}_n$ denotes the group of integers modulo $n$. The value $\sigma(u)$ is is referred to as the modular weight of the vertex $u$. The minimum integer $k$ such that $G$ admits a modular irregular labeling using labels from $\{1, 2, \dots, k\}$ is called the modular irregularity strength of $G$. \\ In this paper, we identify several classes of graphs that exhibit constant modular irregularity strength. In particular, we consider classes of graphs obtained by removing matching from complete graphs, complete bipartite graphs, and complete tripartite graphs. Furthermore, we examine a class of graphs arising from the decomposition of complete multipartite graphs. | ||
| کلیدواژه‌ها | ||
| modular irregularity strength؛ modular irregular labeling؛ complete multipartite graph | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 35 تعداد دریافت فایل اصل مقاله: 31 |
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