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Sibling graphs which are $k$-distance magic | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 اردیبهشت 1405 اصل مقاله (459.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30162.2347 | ||
| نویسندگان | ||
| Sajidha Padinjarakath؛ Edy Tri Baskoro* | ||
| Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia | ||
| چکیده | ||
| This paper investigates $k$-distance magic labeling, for a positive integer $k$, within the framework of sibling graphs, that is, graphs that are both self-centered and antipodal. A $k$-distance magic labeling is a vertex labeling in which the sum of the labels on all vertices at distance $k$ from any given vertex is constant throughout the graph. We establish sufficient conditions for a sibling graph to admit a $k$-distance magic labeling, covering both regular and non-regular cases. Using these conditions, we show that several well-known families of regular sibling graphs of diameter $k$ are $k$-distance magic, including cylindrical grid graphs, cyclic grid graphs, $n$-dimensional hypercubes, circulant graphs, weak Bruhat graphs, and the Möbius--Kantor graph. In addition, we construct examples of irregular sibling graphs that admit a $2$-distance magic labeling. | ||
| کلیدواژهها | ||
| distance magic؛ labeling؛ graph؛ sibling graph | ||
| مراجع | ||
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[10] V. Vilfred, $\sum$-labelled graph and circulant graphs, Ph.D. thesis, University of Kerala, India, Thiruvananthapuram, Kerala, India, 1996. | ||
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آمار تعداد مشاهده مقاله: 28 تعداد دریافت فایل اصل مقاله: 28 |
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