Distance-regular Cayley graphs with small valency

Autor:	Mojtaba Jazaeri, Edwin van Dam
Přispěvatelé:	Econometrics and Operations Research, Research Group: Operations Research
Rok vydání:	2019
Předmět:	Algebra and Number Theory Cayley graph Valency Distance-regular graph Graph Theoretical Computer Science Combinatorics Mathematics::Group Theory distance-regular graph Discrete Mathematics and Combinatorics Geometry and Topology Affine transformation Mathematics
Zdroj:	Ars Mathematica Contemporanea, 17(1), 203-222. Drustvo Matematikov, Fizikov in Astronomov/Society of Mathematicians, Physicists and Astronomers
ISSN:	1855-3974 1855-3966
DOI:	10.26493/1855-3974.1964.297
Popis:	We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most 4 , the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5 , and the Cayley graphs among all distance-regular graphs with girth 3 and valency 6 or 7 . We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some “exceptional” distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphs.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d973e423e6ff4cc2d620495458d3ba16 https://doi.org/10.26493/1855-3974.1964.297 Zobrazit plný text záznamu