On non-normal arc-transitive 4-valent dihedrants

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

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.

• Language: Slovenian
• Keywords: Cayleyjev graf, ločna tranzitivnost, diedrska grupa, Cayley graph, arc transitivity, dihedral group
• Work type: Not categorized
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Year: 2010
• Number of pages: Str. 1485-1498
• Numbering: Vol. 26, no. 8
• PID: 20.500.12556/RUL-84782
• UDC: 519.17
• ISSN on article: 1439-8516
• DOI: 10.1007/s10114-010-8271-8
• COBISS.SI-ID: 1024270932
• Publication date in RUL: 09.09.2016

Record is a part of a journal

• Title: Acta mathematica Sinica
• Shortened title: Acta math. Sin., Engl. ser.
• Publisher: Springer
• ISSN: 1439-8516
• COBISS.SI-ID: 12582489

Secondary language

• Language: English

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: Cayleyjev graf, ločna tranzitivnost, diedrska grupa