Naslov: On strongly regular bicirculants Marušič, Dragan (Avtor)Malnič, Aleksander (Avtor)Šparl, Primož (Avtor) http://dx.doi.org/10.1016/j.ejc.2005.10.010 Angleški jezik Delo ni kategorizirano 1.01 - Izvirni znanstveni članek IAM - Inštitut Andrej Marušič 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. mathematics, graph theory, graph, circulant, bicirculant, automorphism group 2007 str. 891-900 Vol. 28, iss. 3 0195-6698 519.17:512.54 14287705 1143 51 Gradivo ni uvrščeno v področja.

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## Sekundarni jezik

Jezik: Angleški jezik matematika, teorija grafov, graf, cirkulant, bicirkulant, grupa avtomorfizmov

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