The polyomino graphs whose resonance graphs have a 1-degree vertex

Chunhu Sun, Yaxian Zhang and Heping Zhang

Applied Mathematics and Computation, 2024, vol. 474, issue C

Abstract: A polyomino graph is a 2-connected plane graph such that each interior face is a square of side length one. The resonance graph of a polyomino graph P is a graph in which the vertices are the 1-factors of P and two vertices are adjacent provided their corresponding two 1-factors differ in exactly one unite square. In this paper, we determine the polyomino graphs whose resonance graph has a 1-degree vertex by constructing a 4-coordinate system. As consequences we determine the polyomino graphs with a forcing edge and an anti-forcing edge respectively.

Keywords: Polyomino graph; 1-factor; Resonance graph; Forcing edge; Anti-forcing edge (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001760

DOI: 10.1016/j.amc.2024.128704

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