On weakly symmetric graphs of order twice a prime

Cheng, Ying; Oxley, James

doi:10.1016/0095-8956(87)90040-2

Cited by 171 publications

(190 citation statements)

References 9 publications

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“…Since G is arc-transitive on X , by Proposition 2.16, G v either is a 2-group or has order dividing 2 4 · 3 6 . It follows that |G| | 2 5 · 3 6 · p n or |G| = 2 m+1 · p n for some integer m. Let N be a minimal normal subgroup of G. Suppose that N is nonsolvable.…”

Section: Proof Let V ∈ V (X )mentioning

confidence: 99%

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TETRAVALENT s-TRANSITIVE GRAPHS OF ORDER TWICE A PRIME POWER

Zhou

Feng

2010

J. Aust. Math. Soc.

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A graph is s-transitive if its automorphism group acts transitively on s-arcs but not on (s + 1)-arcs in the graph. Let X be a connected tetravalent s-transitive graph of order twice a prime power. In this paper it is shown that s = 1, 2, 3 or 4. Furthermore, if s = 2, then X is a normal cover of one of the following graphs: the 4-cube, the complete graph of order 5, the complete bipartite graph K 5,5 minus a 1-factor, or K 7,7 minus a point-hyperplane incidence graph of the three-dimensional projective geometry PG(2, 2); if s = 3, then X is a normal cover of the complete bipartite graph of order 4; if s = 4, then X is a normal cover of the point-hyperplane incidence graph of the three-dimensional projective geometry PG(2, 3). As an application, we classify the tetravalent s-transitive graphs of order 2 p 2 for prime p.2000 Mathematics subject classification: primary 05C25; secondary 20B25.

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Section: Proof Let V ∈ V (X )mentioning

confidence: 99%

“…Let p be a prime. The classification of s-transitive graphs of order np and of valency 3 or 4 can be obtained from [3,4,27], where 1 ≤ n ≤ 3. Feng et al [10,12,13] classified cubic s-transitive graphs of order np or np 2 with n = 4, 6, 8 or 10.…”

Section: Introductionmentioning

confidence: 99%

TETRAVALENT s-TRANSITIVE GRAPHS OF ORDER TWICE A PRIME POWER

Zhou

Feng

2010

J. Aust. Math. Soc.

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“…We recall that such graphs are already classified when their orders are a prime or the product of two (not necessarily distinct) primes [3,21,22,26,29,28]. Moreover, for p and q primes, the classification of the 4-valent one-regular graphs of order 4p 2 or 2pq is given in [4,31].…”

Section: Introductionmentioning

confidence: 99%

4-valent graphs of order 6p^2 admitting a group of automorphisms acting regularly on arcs

Ghasemi

Spiga

2014

Ars Math. Contemp.

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“…Clearly every tetravalent one-regular graph of order p is a circulant graph. Also, by [7,32,34,37,40,41], every tetravalent one-regular graph of order pq or p 2 is a circulant graph. Furthermore, the classification of tetravalent one-regular graphs of order 2pq is given in [43].…”

Section: Introductionmentioning

confidence: 99%