Extremal degree-based indices of general polyomino chains via dynamic programming
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Montes-y-Morales, Manuel Sigarreta, Sayle Cruz-Suarez, Hugo |
| author_facet | Montes-y-Morales, Manuel Sigarreta, Sayle Cruz-Suarez, Hugo |
| contents | In this paper, we develop a dynamic programming framework for identifying extremal general polyomino chains with respect to degree-based topological indices. As a concrete application, we resolve an open problem posed in 2015 by determining, for any given number of squares, the general polyomino chains that maximize the generalized Randić index with parameter $α=-1$. We show that the extremal configurations depend explicitly on the residue class of the number of squares modulo 4. Beyond this specific result, the proposed dynamic programming approach provides a constructive and systematic methodology for tackling extremal problems in graph theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05684 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extremal degree-based indices of general polyomino chains via dynamic programming Montes-y-Morales, Manuel Sigarreta, Sayle Cruz-Suarez, Hugo Combinatorics 05C10, 05C35, 05C90 In this paper, we develop a dynamic programming framework for identifying extremal general polyomino chains with respect to degree-based topological indices. As a concrete application, we resolve an open problem posed in 2015 by determining, for any given number of squares, the general polyomino chains that maximize the generalized Randić index with parameter $α=-1$. We show that the extremal configurations depend explicitly on the residue class of the number of squares modulo 4. Beyond this specific result, the proposed dynamic programming approach provides a constructive and systematic methodology for tackling extremal problems in graph theory. |
| title | Extremal degree-based indices of general polyomino chains via dynamic programming |
| topic | Combinatorics 05C10, 05C35, 05C90 |
| url | https://arxiv.org/abs/2603.05684 |