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Expected Gutman Index of Markov-Dependent Random Polyomino Chains | ||
| Transactions on Combinatorics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 شهریور 1405 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2026.149467.2373 | ||
| نویسندگان | ||
| Laila Azami؛ Nader Jafari Rad* | ||
| Shahed University | ||
| چکیده | ||
| We introduce a Markov-dependent random model for polyomino chains in which each new square is attached linearly or as a kink according to a stationary two-state Markov chain. This model retains the geometric construction of classical random polyomino chains while allowing consecutive attachment types to be dependent. We develop a direct recursive method based on weighted distance sums associated with the two exposed edges of the terminal square. This method yields exact recursive relations for the auxiliary distance quantities and leads to a closed formula for the expected Gutman index. The independent Bernoulli model is recovered when the two transition probabilities are equal. The deterministic linear and zigzag polyomino chains are also obtained as limiting cases. Our results show that the expected Gutman index depends not only on the stationary frequency of kink attachments, but also on the dependence between consecutive attachments. | ||
| کلیدواژهها | ||
| Gutman index؛ random polyomino chain؛ Markov chain؛ expected value؛ topological index | ||
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آمار تعداد مشاهده مقاله: 9 |
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