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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.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.dam.2018.10.040
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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.

Item Type: Journal Item
Copyright Holders: 2018 Elsevier
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/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 58309
Depositing User: Jozef Širáň
Date Deposited: 14 Dec 2018 14:35
Last Modified: 04 Jul 2020 12:58
URI: http://oro.open.ac.uk/id/eprint/58309
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