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Code for polyomino and computer search of isospectral polyominoes

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Abstract

A new code, binary 2-dimentional code (B2DC), is proposed for polyominoes. An algorithm based on the B2DC and the reverse search method are proposed for enumerating nonisomorphic planar simply connected polyominoes. An enumeration tree and a new father-son relationship are defined for enumerating polyominoes. Then we propose an algorithm to build adjacent matrices and laplacian matrices by B2DCs of polyominoes and search isospectral polyomino graphs by computing characteristic polynomials of those matrices.

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Acknowledgments

The authors are grateful to the anonymous referees for their careful reading and valuable comments to improve this paper. The research is supported by NSFC(11171283).

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, Xinjiang, People’s Republic of China

    Xiaodong Liang, Rui Wang & Ji xiang Meng

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  1. Xiaodong Liang
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  2. Rui Wang
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  3. Ji xiang Meng
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Correspondence to Ji xiang Meng.

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Liang, X., Wang, R. & Meng, J.x. Code for polyomino and computer search of isospectral polyominoes. J Comb Optim 33, 254–264 (2017). https://doi.org/10.1007/s10878-015-9953-z

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