A CLASSIFICATION OF THE CUBIC SEMISYMMETRIC GRAPHS OF ORDER 34p² (original) (raw)

A CLASSIFICATION OF SEMISYMMETRIC CUBIC GRAPHS OF ORDER 28p&sup2

Journal of the Indonesian Mathematical Society, 2010

A graph is said to be semisymmetric if its full automorphism group actstransitively on its edge set but not on its vertex set. In this paper, we prove thatthere is only one semisymmetric cubic graph of order 28p2, where p is a prime.DOI : http://dx.doi.org/10.22342/jims.16.2.38.139-143

Semisymmetric cubic graphs of orders 36p, 36p2

Filomat, 2013

A cubic graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. The semisymmetric cubic graphs of orders 6p and 6p 2 were classified in (Com. in Algebra, 28 (6) (2000) 2685-2715) and (Science in China Ser. A Mathematics, 47 (2004) No.1 1-17), respectively. In this paper we first classify all connected cubic semisymmetric graphs of order 36p for each prime p and also classify all connected cubic semisymmetric graphs of order 36p 2 , where p 5 and 7 is a prime.

Cubic semisymmetric graphs of order

Discrete Mathematics, 2010

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 2p or 2p 2 for a prime p and by Malnič, et al. [A. Malnič, D. Marušič, C.Q. Wang, Cubic edge-transitive graphs of order 2p 3 , Discrete Math. 274 (2004) 187-198], there exists a unique cubic semisymmetric graph of order 2p 3 , the so-called Gray graph of order 54. In this paper it is shown that a connected cubic semisymmetric graph of order 6p 3 exists if and only if p − 1 is divisible by 3. There are exactly two such graphs for a given order, which are constructed explicitly.

Semisymmetric Cubic Graphs of Order 4p

2009

An regular graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper we prove that for every prime p(6= 5), there is no semisymmetric cubic graph of order 4pn, where n ≥ 1. 2000 Mathematics Subject Classification: 05C25, 20B25.

Semisymmetric cubic graphs of order 16p 2

Proceedings - Mathematical Sciences, 2010

An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs of order 16p 2 . It is shown that for every odd prime p, there exists a semisymmetric cubic graph of order 16p 2 and its structure is explicitly specified by giving the corresponding voltage rules generating the covering projections.

CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 8p2

Bulletin of The Australian Mathematical Society, 2008

A regular graph Γ is said to be semisymmetric if its full automorphism group acts transitively on its edge-set but not on its vertex-set. It was shown by Folkman [5] that a regular edge-transitive graph of order 2p or 2p 2 is necessarily vertex-transitive, where p is a prime. In this paper, it is proved that there is no connected semisymmetric cubic graph of order 4p 2 , where p is a prime.

Cubic edge-transitive graphs of order 4p2

A regular graph Γ is said to be semisymmetric if its full automorphism group acts transitively on its edge-set but not on its vertex-set. It was shown by Folkman [5] that a regular edgetransitive graph of order 2p or 2p 2 is necessarily vertex-transitive, where p is a prime. In this paper, it is proved that there is no connected semisymmetric cubic graph of order 4p 2 , where p is a prime.

CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 8 p2

Bulletin of The Australian Mathematical Society, 2008

A regular graph Γ is said to be semisymmetric if its full automorphism group acts transitively on its edge-set but not on its vertex-set. It was shown by Folkman [5] that a regular edge-transitive graph of order 2p or 2p 2 is necessarily vertex-transitive, where p is a prime. In this paper, it is proved that there is no connected semisymmetric cubic graph of order 4p 2 , where p is a prime.

Classifying cubic edge-transitive graphs of order 8p

Proceedings - Mathematical Sciences, 2009

A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman (J. Combin. Theory 3 (1967) 215-232) that a regular edge-transitive graph of order 2p or 2p 2 is necessarily vertex-transitive. In this paper, an extension of his result in the case of cubic graphs is given. It is proved that, every cubic edge-transitive graph of order 8p is symmetric, and then all such graphs are classified.