On strongly regular bicirculants

Malnič, Aleksander; Marušič, Dragan; Šparl, Primož

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Title:	On strongly regular bicirculants
Authors:	ID Malnič, Aleksander (Author) ID Marušič, Dragan (Author) ID Šparl, Primož (Author)
Files:	http://dx.doi.org/10.1016/j.ejc.2005.10.010
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	An $n$ -bicirculantis a graph having an automorphism with two orbits of length $n$ and no other orbits. This article deals with strongly regular bicirculants. It is known that for a nontrivial strongly regular $n$ -bicirculant, $n$ odd, there exists a positive integer m such that $n=2m^2+2m+1▫$. Only three nontrivial examples have been known previously, namely, for ▫$m=1,2$ and 4. Case $m=1$ gives rise to the Petersen graph and its complement, while the graphs arising from cases $m=2$ and $m=4$ are associated with certain Steiner systems. Similarly, if $n$ is even, then $n=2m^2$ for some $m \ge 2$ . Apart from a pair of complementary strongly regular 8-bicirculants, no other example seems to be known. A necessary condition for the existence of a strongly regular vertex-transitive $p$ -bicirculant, $p$ a prime, is obtained here. In addition, three new strongly regular bicirculants having 50, 82 and 122 vertices corresponding, respectively, to $m=3,4$ and 5 above, are presented. These graphs are not associated with any Steiner system, and together with their complements form the first known pairs of complementary strongly regular bicirculants which are vertex-transitive but not edge-transitive.
Keywords:	mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Year of publishing:	2007
Number of pages:	str. 891-900
Numbering:	Vol. 28, iss. 3
PID:	20.500.12556/RUP-7721
ISSN:	0195-6698
UDC:	519.17:512.54
COBISS.SI-ID:	14287705
Publication date in RUP:	03.04.2017
Views:	6614
Downloads:	92
Metadata:
:	MALNIČ, Aleksander, MARUŠIČ, Dragan and ŠPARL, Primož, 2007, On strongly regular bicirculants. [online]. 2007. Vol. 28, no. 3, p. 891–900. [Accessed 4 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.ejc.2005.10.010 Copy citation