A note on transitive permutation groups of degree twice a prime

Potočnik, Primož; Šajna, Mateja

doi:10.26493/1855-3974.80.880

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…Thus we may assume that (1, 1, 1, …, 1)∉ G . Then, by 21, Theorem 6.2 (see also 34, Theorem 1) and since ρ∈ G , there exists ε = (1, 1, 0, …)∈ E ∩ G .…”

Section: Cubic Non‐cayley Vertex‐transitive Graphs Of Order 4p2mentioning

confidence: 87%

On cubic non‐Cayley vertex‐transitive graphs

Kutnar

Marušič

Zhang

2011

Journal of Graph Theory

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Abstract:In 1983, the second author [D. Marušič, Ars Combinatoria 16B (1983), 297-302] asked for which positive integers n there exists a nonCayley 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.

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“…Thus we may assume that (1, 1, 1, …, 1)∉ G . Then, by 21, Theorem 6.2 (see also 34, Theorem 1) and since ρ∈ G , there exists ε = (1, 1, 0, …)∈ E ∩ G .…”

Section: Cubic Non‐cayley Vertex‐transitive Graphs Of Order 4p2mentioning

confidence: 87%

On cubic non‐Cayley vertex‐transitive graphs

Kutnar

Marušič

Zhang

2011

Journal of Graph Theory

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“…The rather long and technical proof can be found in [16]. [16].) Let p be an odd prime, V a set of size 2p, G a transitive permutation group on V , and P a Sylow p-subgroup of G. Then P has two orbits on V , each of size p. Suppose further that the orbits of P are not blocks of imprimitivity for G, but that there exists a G-invariant partition B of V into blocks of size 2.…”

Section: Homogeneously Almost Self-complementary Graphs Of Order 4pmentioning

confidence: 98%

Brick assignments and homogeneously almost self-complementary graphs

Potočnik

Šajna

2009

Journal of Combinatorial Theory, Series B

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A graph is called almost self-complementary if it is isomorphic to the graph obtained from its complement by removing a 1-factor. In this paper, we study a special class of vertex-transitive almost self-complementary graphs called homogeneously almost selfcomplementary. These graphs occur as factors of symmetric index-2 homogeneous factorizations of the "cocktail party graphs" K 2n − nK 2 . We construct several infinite families of homogeneously almost self-complementary graphs, study their structure, and prove several classification results, including the characterization of all integers n of the form n = p r and n = 2p with p prime for which there exists a homogeneously almost self-complementary graph on 2n vertices.

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