István Kovács (Author), Boštjan Kuzman (Author), Aleksander Malnič (Author)

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;Cayley graph;arc transitivity;dihedral group;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL PEF - Faculty of Education
UDC: 519.17
COBISS: 1024270932 Link will open in a new window
ISSN: 1439-8516
Views: 760
Downloads: 287
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Other data

Secondary language: English
Secondary 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.
Secondary keywords: Cayleyjev graf;ločna tranzitivnost;diedrska grupa;
Type (COBISS): Not categorized
Pages: str. 1485-1498
Volume: ǂVol. ǂ26
Issue: ǂno. ǂ8
Chronology: 2010
DOI: 10.1007/s10114-010-8271-8
ID: 1477165