On the reflexive edge strength in zigzag graphs

Ibrahim, Muhammad; Khan, Muhammad Javed Azhar; Hasni, Roslan; Kooi Kuan, Yoong; Agustin, Ika Hesti

doi:10.22108/toc.2026.146523.2322

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	On the reflexive edge strength in zigzag graphs
Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 05 خرداد 1405 اصل مقاله (499.9 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2026.146523.2322
نویسندگان
Muhammad Ibrahim¹؛ Muhammad Javed Azhar Khan¹؛ Roslan Hasni^* ²؛ Yoong Kooi Kuan³؛ Ika Hesti Agustin⁴
¹Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
²Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
³School of Computing and Data Science, Xiamen University Malaysia, 43900 Sepang, Selangor, Malaysia
⁴Mathematics Department, University of Jember, Jl. Kalimantan N0. 37 Sumbersari Jember, East Java 68121, Indonesia
چکیده
Let $G$ be a simpple graph. The total $k$-labeling of $G$ is the assignments of a non-negative integer from the set $\{0,2,\ldots,2\lfloor k/2\rfloor\}$ to the vertices and a positive integer from the set $\{1,2,\ldots,k\}$ to the edges of a graph $G$. It is called an edge irregular reflexive $k$-labeling of the graph $G$ if the weights of any two different edges are distinct, where the edge weight is the sum of the label of the edge itself and the labels of its two end vertices. The minimum value $k$ for which the graph $G$ has an edge irregular reflexive $k$-labeling is called the reflexive edge strength of $G$. In this paper, we determine the exact value of the reflexive edge strength for the zigzag graph $Z_{m}^{n}$, where $n \geq 2 $ and $m \geq 3$.
کلیدواژه‌ها
Edge irregular reflexive labeling؛ reflexive edge strength؛ zigzag graph

مراجع
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On the reflexive edge strength in zigzag graphs