Laplacian of a Graph Covering and Its Applications

  • Deqiong Li
  • Yaoping Hou


Let G be a finite graph and \(\overline{G}\) be any graph covering over G. By applying the representation theory of symmetric groups, the Laplacian characteristic polynomial and the normalized Laplacian characteristic polynomial of \(\overline{G}\) are investigated. As applications, adopting the algebra method the Kirchhoff index, the multiplicative degree-Kirchhoff index and the complexity of any connected covering over a connected graph are derived.


Graph covering Laplacian matrix Normalized Laplacian matrix Resistance distance Kirchhoff index Complexity 

Mathematics Subject Classification




This project was supported by the National Natural Science Foundation of China (No. 11571101). The authors are grateful to the anonymous referees for their valuable comments and helpful suggestions, which have considerably improved the presentation of this paper.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Key Laboratory of HPCSIP, Ministry of Education of China, College of Mathematics and Computer ScienceHunan Normal UniversityChangshaChina
  2. 2.College of Mathematics and ComputationHunan Science and Technology UniversityXiangtanChina

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