Orienting and separating distance-transitive graphs

Ítalo José Dejter

Abstract


It is shown that exactly 7 distance-transitive cubic graphs among the existing 12 possess a particular ultrahomogeneous property with respect to oriented cycles realizing the girth that allows the construction of a related Cayley digraph with similar ultrahomogeneous properties in which those oriented cycles appear minimally ''pulled apart'', or ''separated'' and whose description is truly beautiful and insightful. This work is proposed as the initiation of a study of similar ultrahomogeneous properties for distance-transitive graphs in general with the aim of generalizing to constructions of similar related ''separator'' Cayley digraphs.

Keywords


distance-transitive graph, ultrahomogeneous graph, Cayley graph

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DOI: https://doi.org/10.26493/1855-3974.235.446

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications