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On strongly regular bicirculantsMalnič, Aleksander ; Marušič, Dragan ; Šparl, PrimožAn ▫$n$▫-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.Source: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 28, iss. 3, 2007, str. 891-900)Type of material - article, component partPublish date - 2007Language - englishCOBISS.SI-ID - 14287705
Author
Malnič, Aleksander |
Marušič, Dragan |
Šparl, Primož
Topics
matematika |
teorija grafov |
graf |
cirkulant |
bicirkulant |
grupa avtomorfizmov |
mathematics |
graph theory |
graph |
circulant |
bicirculant |
automorphism group
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source: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 28, iss. 3, 2007, str. 891-900)
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Database name | Field | Year |
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Malnič, Aleksander | 02507 |
Marušič, Dragan | 02887 |
Šparl, Primož | 23341 |
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