Exact Dominion of the Prism Graph: Enumeration by Congruence Class via Cyclic Words

Julian Allagan, Vladimir Deriglazov, Rogelio N. Lopez-Bonilla and Kevin Pereyra

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-7

Abstract: Let Gn=Cn□P2 be the prism graph on 2n vertices. The dominionζGn counts the minimum dominating sets of Gn. Encoding column selections as cyclic words over a quaternary alphabet converts domination into explicit local adjacency constraints, reducing the count of minimum dominating sets to the enumeration of minimum-weight admissible words. This yields closed-form formulas for ζGn for all n≥3, stratified by n mod 4, with the exceptional cases n∈3,6 confirmed by exhaustive computation.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1411005

DOI: 10.1155/ijmm/1411005

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