| 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: | 02.04.2017 |
|---|
| Views: | 5112 |
|---|
| Downloads: | 89 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
