The girth of Cayley graphs over Sylow 2-subgroups of the symmetric groups S2n with diagonal bases

Bartłomiej Pawlik

doi:10.1142/S0219498819502372

The girth of Cayley graphs over Sylow 2-subgroups of the symmetric groups S_2n with diagonal bases

Bartłomiej Pawlik

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

Abstract

A diagonal base of a Sylow 2-subgroup Pn(2) of symmetric group S2n is a minimal generating set of this subgroup consisting of elements with only one nonzero coordinate in the polynomial representation. For different diagonal bases, Cayley graphs over Pn(2) may have different girths (i.e. minimal lengths of cycles). In this paper, all possible values of girths of Cayley graphs over Pn(2) with diagonal bases are calculated. A criterion for whenever such Cayley graph has girth equal to 4 is presented.

Original language	English
Article number	1950237
Journal	Journal of Algebra and its Applications
Volume	18
Issue number	12
DOIs	https://doi.org/10.1142/S0219498819502372
Publication status	Published - 1 Dec 2019

Keywords

Cayley graph
Sylow p -subgroup
girth of graph
wreath product

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

Access to Document

10.1142/S0219498819502372

Cite this

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abstract = "A diagonal base of a Sylow 2-subgroup Pn(2) of symmetric group S2n is a minimal generating set of this subgroup consisting of elements with only one nonzero coordinate in the polynomial representation. For different diagonal bases, Cayley graphs over Pn(2) may have different girths (i.e. minimal lengths of cycles). In this paper, all possible values of girths of Cayley graphs over Pn(2) with diagonal bases are calculated. A criterion for whenever such Cayley graph has girth equal to 4 is presented.",

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KW - Sylow p -subgroup

KW - girth of graph

KW - wreath product

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