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Constructing Graphs Which are Permanental Cospectral and Adjacency Cospectral

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Abstract

Two graphs are adjacency cospectral (respectively, permanental cospectral) if they have the same adjacency spectrum (respectively, permanental spectrum). In this paper, we present a new method to construct new adjacency cospectral and permanental cospetral pairs of graphs from smaller ones. As an application, we obtain an infinite family of pairs of Cartesian product graphs which are adjacency cospectral and permanental cospetral.

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Acknowledgements

We would like to thank the referees for their helpful recommendations. The research is supported by the National Natural Science Foundation of China (No. 11761056), the Natural Science Foundation of Qinghai Province (2016-ZJ-947Q), the Ministry of Education Chunhui Project (No. Z2017047) and High-level Personnel of Scientific Research Project of QHMU(2016XJG07).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qinghai Nationalities University, Xining, 810007, Qinghai, People’s Republic of China

    Tingzeng Wu

  2. Department of Mathematics, West Virginia University, Morgantown, WV, USA

    Hong-Jian Lai

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  1. Tingzeng Wu
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  2. Hong-Jian Lai
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Correspondence to Tingzeng Wu.

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Wu, T., Lai, HJ. Constructing Graphs Which are Permanental Cospectral and Adjacency Cospectral. Graphs and Combinatorics 34, 1713–1721 (2018). https://doi.org/10.1007/s00373-018-1963-z

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  • DOI: https://doi.org/10.1007/s00373-018-1963-z

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