20.500.12556/RUP-7721
On strongly regular bicirculants
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
matematika
teorija grafov
graf
cirkulant
bicirkulant
grupa avtomorfizmov
true
true
false
Angleški jezik
Angleški jezik
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2016-04-08 16:46:25
2017-04-03 08:13:36
2024-03-01 13:33:23
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2007
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str. 891-900
iss. 3
Vol. 28
2007
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NiDoloceno
NiDoloceno
NiDoloceno
0000-00-00
0000-00-00
0000-00-00
0195-6698
519.17:512.54
25427968
14287705
http://dx.doi.org/10.1016/j.ejc.2005.10.010
1
https://repozitorij.upr.si/Dokument.php?lang=slv&id=7721
Inštitut Andrej Marušič
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