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Title:On non-normal arc-transitive 4-valent dihedrants
Authors:Kovács, István (Author)
Kuzman, Boštjan (Author)
Malnič, Aleksander (Author)
Files:URL http://www.springerlink.com/content/91474375p0273m92/fulltext.pdf
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:Let ▫$X$▫ be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group ▫$D_n$▫ such that ▫$X$▫ is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within ▫$D_n$▫. It is shown that ▫$X$▫ is isomorphic either to the lexicographic product ▫$C_n[2K_1]$▫ with ▫$n \geq 4$▫ even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.
Keywords:Cayley graph, arc transitivity, dihedral group
Year of publishing:2010
Number of pages:str. 1485-1498
Numbering:Vol. 26, no. 8
ISSN:1439-8516
UDC:519.17
COBISS_ID:1024270932 Link is opened in a new window
Views:1734
Downloads:37
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Secondary language

Language:English
Abstract:Naj bo ▫$X$▫ povezan nenormalen 4-valenten ločno-tranzitiven Cayleyev graf diedrske grupe ▫$D_n$▫, tako da je ▫$X$▫ dvodelen in ustrezna biparticija vozlišč ustreza dvema orbitama ciklične podgrupe znotraj ▫$D_n$▫. Dokazano je, da je tedaj ▫$X$▫ izomorfen bodisi leksikografskemu produktu ▫$C_n[2K_1]$▫ za ▫$n \geq 4$▫ sodo, bodisi enemu od petih posebnih grafov na 10, 14, 26, 28 oz. 30 vozliščih.
Keywords:Cayleyjev graf, ločna tranzitivnost, diedrska grupa

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