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Pebbling in Sierpiński type graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 فروردین 1404 اصل مقاله (549.69 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30166.2343 | ||
| نویسندگان | ||
| A. Sagaya Suganya* 1؛ M. Joice Punitha2 | ||
| 1Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science & Technology, Chennai, India | ||
| 2Department of Mathematics, Bharathi Women’s College, Chennai, India | ||
| چکیده | ||
| Graph pebbling is a network optimization technique for the movement of resources in transit. A pebbling move in a connected graph $G$ can be defined as a distribution of pebbles on the vertices of a graph, which involves removing two pebbles from a vertex, placing one pebble on one of its adjacent vertices, and discarding the other pebble. For a graph $G$, the pebbling number $f(G)$ is the minimum number of pebbles required such that one pebble is moved to any arbitrary vertex of the graph $G$. Fractals are described as intricate patterns that are identical at different dimensions or identical in all dimensions. In this paper, the strategy of pebbling is applied to Sierpi'nski graphs which are well known fractals and several critical points are scrutinized and verified for Generalized Sierpi'nski graph $S(G,t), t \geq 2$, Sierpi'nski graph $S(K_n, t)$, $t \geq 1$, $n \geq 2$ and Sierpi'nski triangle graph $S_m$, $m \geq 2$. | ||
| کلیدواژهها | ||
| Fractal؛ Pebbling؛ Generalized Sierpiński graph؛ Sierpiński triangle graph | ||
| مراجع | ||
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