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Constructing Graphs Which are Permanental Cospectral and Adjacency Cospectral

  • Tingzeng Wu
  • Hong-Jian Lai
Original Paper
  • 2 Downloads

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.

Keywords

Permanental polynomial Characteristic polynomial Permanental cospectral Adjacency cospectral 

Mathematics Subject Classification

05C31 05C50 15A15 

Notes

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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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsQinghai Nationalities UniversityXiningPeople’s Republic of China
  2. 2.Department of MathematicsWest Virginia UniversityMorgantownUSA

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