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Exploring the Precise Edge Irregularity Strength of Generalized Arithmetic and Geometric Staircase Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 اسفند 1402 اصل مقاله (971.7 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28992.1804 | ||
| نویسندگان | ||
| Yeni Susanti* ؛ Muhammad Nurul Huda؛ Ramadhani Latief Firmansyah | ||
| Department of Mathematics, Universitas Gadjah Mada, Indonesia | ||
| چکیده | ||
| In the context of a finite undirected graph $\zeta$, an edge irregular labelling is defined as a labelling of its vertices with some labels in such a way that each edge has a unique weight, which is determined by the sum of the labels of its endpoints. The main objective of this study is to determine the smallest positive integer $n$ for which it is possible to assign a total edge irregular labelling to $\zeta$ with $n$ as the biggest label. This investigation focuses particularly on cases where $\zeta$ represents the generalized arithmetic and generalized geometric staircase graphs. Within this paper, the definition of generalized geometric staircase graph is proposed. Moreover, we not only establish the edge irregularity strength of these two kind of graphs but also present a method for creating the corresponding edge irregular labelling. | ||
| کلیدواژه‌ها | ||
| irregular labeling؛ staircase graphs؛ total edge irregularity strength | ||
| مراجع | ||
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