Journal of Mathematical Chemistry

, Volume 51, Issue 2, pp 603–619

On maximal resonance of polyomino graphs

Original Paper

DOI: 10.1007/s10910-012-0104-9

Cite this article as:
Liu, S. & Ou, J. J Math Chem (2013) 51: 603. doi:10.1007/s10910-012-0104-9


A polyomino graph is a finite plane 2-connected bipartite graph every interior face of which is bounded by a regular square of side length one. Let k be a positive integer, a polyomino graph G is k-resonant if the deletion of any ik vertex-disjoint squares from G results in a graph either having perfect matchings or being empty. If graph G is k-resonant for any integer k ≥ 1, then it is called maximally resonant. All maximally resonant polyomino graphs are characterized in this work. As a result, the least integer k such that a k-resonant polyomino graph is maximally resonant is determined.


Polyomino graph k-resonance Maximal resonance 

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsWuyi UniversityJiangmenPeople’s Republic of China

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