Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach

Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach

We examine the existing constructions of the smallest known vertex‐transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of...

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Veröffentlicht in:Journal of graph theory 2011-12, Vol.68 (4), p.265-284
Hauptverfasser: Loz, Eyal, Mačaj, Martin, Miller, Mirka, Šiagiová, Jana, Širáň, Jozef, Tomanová, Jana
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cage
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container_end_page 284
container_issue 4
container_start_page 265
container_title Journal of graph theory
container_volume 68
creator Loz, Eyal
Mačaj, Martin
Miller, Mirka
Šiagiová, Jana
Širáň, Jozef
Tomanová, Jana
description We examine the existing constructions of the smallest known vertex‐transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex‐transitive graphs of a given degree and girth 6 and relate their constructions to near‐difference sets. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:265‐284, 2011
doi_str_mv 10.1002/jgt.20556
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subjects cage
degree
girth
graph
title Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach
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