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Sugeng, K.A., Barack, Z.Z., Augurius, M., Yehezkiel, L., John, P., Semaničová-Feňovčíková, A., Bača, M., Mella, L.. (1405). Graphs with Constant Modular Irregularity Strength. , (), -. doi: 10.22049/cco.2026.30751.2607
K.A. Sugeng; Z.Z. Barack; M. Augurius; L. Yehezkiel; P. John; A. Semaničová-Feňovčíková; M. Bača; L. Mella. "Graphs with Constant Modular Irregularity Strength". , , , 1405, -. doi: 10.22049/cco.2026.30751.2607
Sugeng, K.A., Barack, Z.Z., Augurius, M., Yehezkiel, L., John, P., Semaničová-Feňovčíková, A., Bača, M., Mella, L.. (1405). 'Graphs with Constant Modular Irregularity Strength', , (), pp. -. doi: 10.22049/cco.2026.30751.2607
Sugeng, K.A., Barack, Z.Z., Augurius, M., Yehezkiel, L., John, P., Semaničová-Feňovčíková, A., Bača, M., Mella, L.. Graphs with Constant Modular Irregularity Strength. , 1405; (): -. doi: 10.22049/cco.2026.30751.2607

Graphs with Constant Modular Irregularity Strength

Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 آبان 1405
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
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