Classifying cubic edge-transitive graphs of order 8p (original) (raw)

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.

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.

A CLASSIFICATION OF THE CUBIC SEMISYMMETRIC GRAPHS OF ORDER 34p²

Journal of the Indonesian Mathematical Society, 2012

A simple undirected graph is called semisymmetric if it is regular and edge transitive but not vertex-transitive. In this paper, we classify all connected cubic semisymmetric graph of order 34p², where p be a prime.DOI : http://dx.doi.org/10.22342/jims.17.1.9.11-15

ON THE CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 58p258p258p2

Journal of the Indonesian Mathematical Society, 2015

A graph is called edge-transitive, if its full automorphism group acts transitively on its edge set. In this paper, we inquire the existence of connected edge-transitive cubic graphs of order 58p 2 for each prime p. It is shown that only for p = 29, there exists a unique edge-transitive cubic graph of order 58p 2 .

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.

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.

On cubic non-Cayley vertex-transitive graphs

Journal of Graph Theory, 2012

In 1983, the second author [D. Marušič, Ars Combinatoria 16B (1983), 297-302] asked for which positive integers n there exists a non-Cayley vertex-transitive graph on n vertices. (The term non-Cayley numbers has later been given to such integers.) Motivated by this problem, Feng [Discrete Math 248 (2002), 265-269] asked to determine the smallest valency ϑ(n) among valencies of non-Cayley vertex-transitive graphs of order n. As cycles are clearly Cayley graphs, ϑ(n) ≥ 3 for any non-Cayley number n. In this paper a goal is set to determine those non-Cayley numbers n for which ϑ(n) = 3, and among the latter to determine those for which the generalized Petersen graphs are the only non-Cayley vertex-transitive Contract grant sponsors: Agencija za raziskovalno dejavnost Republike Slovenije, research program P1-0285 (to K. K., D. M., C. Z.); Agencija za raziskovalno dejavnost Republike Slovenije, proj. mladi raziskovalci (to C. Z.).

A more detailed classification of symmetric cubic graphs

2000

A graph is symmetric if its automorphism group acts transitively on the arcs of , and s-regular if its automorphism group acts regularly on the set of s-arcs of . Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. Djokoviÿc and Miller (1980) proved that there are seven types of arc-transitive