| Title: | On strongly regular bicirculants |
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| Authors: | ID Malnič, Aleksander (Author)
ID Marušič, Dragan (Author)
ID Šparl, Primož (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.ejc.2005.10.010
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| 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. |
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| Keywords: | mathematics, graph theory, graph, circulant, bicirculant, automorphism group |
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| Year of publishing: | 2007 |
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| Number of pages: | str. 891-900 |
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| Numbering: | Vol. 28, iss. 3 |
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| PID: | 20.500.12556/RUP-7721  |
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| ISSN: | 0195-6698 |
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| UDC: | 519.17:512.54 |
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| COBISS.SI-ID: | 14287705 |
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| Publication date in RUP: | 03.04.2017 |
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| Views: | 3537 |
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| Downloads: | 88 |
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