Resumo

GONZALEZ-VAZQUEZ, Herlinda; LOPEZ-RAMIREZ, Cristina; BELLO-LOPEZ, Pedro  e  ITA-LUNA, Guillermo de. Branching and Pruning Algorithm for Computing the Merrifield-Simmons Index on Polygonal Grids. Comp. y Sist. [online]. 2024, vol.28, n.4, pp.2171-2182.  Epub 25-Mar-2025. ISSN 2007-9737.  https://doi.org/10.13053/cys-28-4-5300.

In this paper, we present the molecular structure of benzene as a regular hexagonal ring and an isomorphic hexagonal lattice, a molecular structure introduced by Merrifield-Simmons ($MS$) in 1989. The $MS$ index, a topological index used in mathematical chemistry, is the number of independent sets of a graph $G$. This index plays a crucial role in our understanding of complex molecular structures. The strategy to compute the $MS$ index involves the construction of a Hamiltonian trajectory in the input graph. These structures are discussed in fields such as theoretical and computational chemistry. Therefore, we propose a novel branch and bound method for counting independent sets on polygonal benzenoid meshes, highlighting its importance in the study of the analysis of complex molecular structures and its applicability in interdisciplinary scientific fields.

Palavras-chave : Benzenoid; independent sets; Hamiltonian path.

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