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arXiv · 2603.05684

Extremal degree-based indices of general polyomino chains via dynamic programming

Manuel Montes-y-Morales·Sayle Sigarreta·Hugo Cruz-Suarez
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Abstract

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 Randi\'c index with parameter $\alpha=-1$. 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.

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Manuel Montes-y-Morales, Sayle Sigarreta, Hugo Cruz-Suarez. 2026-03-05. Extremal degree-based indices of general polyomino chains via dynamic programming. https://arxiv.org/abs/2603.05684

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