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Cubic semisymmetric graphs of order
- Source :
-
Discrete Mathematics . Sep2010, Vol. 310 Issue 17/18, p2345-2355. 11p. - Publication Year :
- 2010
-
Abstract
- Abstract: A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. By Folkman [J. Folkman, Regular line-symmetric graphs, J. Combin Theory 3 (1967) 215–232], there is no semisymmetric graph of order or for a prime and by Malnič, et al. [A. Malnič, D. Marušič, C.Q. Wang, Cubic edge-transitive graphs of order , Discrete Math. 274 (2004) 187–198], there exists a unique cubic semisymmetric graph of order , the so-called Gray graph of order 54. In this paper it is shown that a connected cubic semisymmetric graph of order exists if and only if is divisible by 3. There are exactly two such graphs for a given order, which are constructed explicitly. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 310
- Issue :
- 17/18
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 51942157
- Full Text :
- https://doi.org/10.1016/j.disc.2010.05.018