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Half-arc-transitive graphs of order ▫$4p$▫ of valency twice a primeWang, Xiuyun ; Feng, Yan-QuanA graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let ▫$p$▫ be a prime. Cheng and Oxley [On weakly symmetric graphs of order twice a ... prime, J. Combin. Theory B 42 (1987),196-211] proved that there is no half-arc-transitive graph of order ▫$2p$▫, and Alspach and Xu [1/2-transitive graphs of order ▫$3p$▫, J. Algebraic Combin. 3 (1994), 347-355] classified half-arc-transitive graphs of order ▫$3p$▫. In this paper we classify half-arc-transitive graphs of order ▫$4p$▫ of valency ▫$2q$▫ for each prime ▫$q \ge 5$▫. It is shown that such graphs exist if and only if ▫$p - 1$▫ is divisible by ▫$4q$▫. Moreover, for such ▫$p$▫ and ▫$q$▫ a unique half-arc-transitive graph of order ▫$4p$▫ and valency ▫$2q$▫ exists and this graph is a Cayley graph.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 3, no. 2, 2010, str. 151-163)Type of material - article, component part ; adult, seriousPublish date - 2010Language - englishCOBISS.SI-ID - 15859033
Author
Wang, Xiuyun |
Feng, Yan-Quan
Topics
matematika |
teorija grafov |
Cayleyjevi grafi |
tranzitivni grafi |
mathematics |
graph theory |
Cayley graph |
half-arc-transitive graph |
transitive graph
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