An algebraic approach to lifts of digraphs

Dalfó, C.; Fiol, M. A.; Miller, M.; Ryan, J. and Širáň, J. (2019). An algebraic approach to lifts of digraphs. Discrete Applied Mathematics, 269 pp. 68–76.

DOI: https://doi.org/10.1016/j.dam.2018.10.040

Abstract

We present some applications of a new matrix approach for studying the properties of the lift $\Gamma^{\alpha}$ of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, we completely determine the spectrum of $\Gamma^{\alpha}$. As some examples of our technique, we study some basic properties of the Alegre digraph, and completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and the Hoffman–Singleton graph.

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About

  • Item ORO ID
  • 58309
  • Item Type
  • Journal Item
  • ISSN
  • 0166-218X
  • Project Funding Details
  • Funded Project NameProject IDFunding Body
    Not SetAPVV0136/12Not Set
    Not SetAPVV-15-0220Not Set
    Not SetVEGA1/0026/16Not Set
    Not SetVEGA1/0142/17Not Set
  • Keywords
  • Digraph; Adjacency matrix; Regular partition; Quotient digraph; Abelian group; Spectrum; Voltage digraphs; Lifted digraph; Generalized Petersen graph
  • Academic Unit or School
  • Faculty of Science, Technology, Engineering and Mathematics (STEM)
  • Copyright Holders
  • © 2018 Elsevier
  • Depositing User
  • Jozef Širáň

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