Some computational aspects of solvable regular covers of graphs. (September 2015)

• Record Type: Journal Article
• Authors: Požar, Rok
• Is Part Of: Journal of symbolic computation. Volume 70(2015)
• Page Start: 1
• Page End: 13
• Publication Date: 2015-09
• Subjects: Algorithm -- Solvable regular cover -- Voltages -- Covering projection -- Experimental comparison -- Graph -- Group extension -- Lifting automorphisms; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.09.023
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Given a connected graph X and a group G of its automorphisms we first introduce an approach for constructing all pairwise nonequivalent connected solvable regular coverings ℘ : X ˜ → X (that is, with a solvable group of covering transformations CT ( ℘ ) ) along which G lifts, up to a prescribed order n of X ˜ . Next, given a connected solvable regular covering ℘ : X ˜ → X by means of voltages and a group G ≤ Aut ( X ) that lifts along ℘, we consider algorithms for testing whether the lifted group G ˜ is a split extension of CT ( ℘ ) . In computational group theory, methods for testing whether a given extension of permutation groups splits are known. However, in order to apply the existing algorithms, X ˜ together with CT ( ℘ ) and G ˜ need to be constructed in the first place, which is far from optimal. Recently, an algorithm avoiding such explicit constructions has been proposed by Malnič and Požar (submitted for publication) . We here provide additional details about this algorithm and investigate its performance compared to the one using explicit constructions. To this end, a concrete dataset of solvable regular covers of graphs has been generated by the algorithm mentioned in the first paragraph.