Cubic semisymmetric graphs of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si68.gif" display="inline" overflow="scroll"><mml:mn>6</mml:mn><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>

Feng, Yan-Quan; Ghasemi, Mohsen; Wang, Changqun

doi:10.1016/j.disc.2010.05.018

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Cited by 6 publications

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“…1. Using GAP software, we easily obtain the stabilizer of 1 under T 12 as (2, 4)(3, 5)(7, 9)(8, 10), (3,5,4) (8,10,9) .…”

Section: Proof Since Gmentioning

confidence: 99%

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Discuss. Math. Graph Theory

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A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be an arbitrary prime. Folkman proved [Regular line-symmetric graphs, J. Combin. Theory 3 (1967) 215-232] that there is no semisymmetric graph of order 2p or 2p 2 . In this paper an extension of his result in the case of cubic graphs of order 20p 2 is given. We prove that there is no connected cubic semisymmetric graph of order 20p 2 or, equivalently, that every connected cubic edge-transitive graph of order 20p 2 is necessarily symmetric.

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“…1. Using GAP software, we easily obtain the stabilizer of 1 under T 12 as (2, 4)(3, 5)(7, 9)(8, 10), (3,5,4) (8,10,9) .…”

Section: Proof Since Gmentioning

confidence: 99%

“…Connected cubic semisymmetric graphs of orders 4p 3 , 6p 2 , 6p 3 , 8p 3 , 10p 3 , 18p n have been classified in [3,8,11,13] and [22].…”

Section: Introductionmentioning

confidence: 99%