The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases

Bartłomiej Pawlik

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arXiv · 1806.08604

The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases

Bartłomiej Pawlik

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Abstract

A diagonal base of a Sylow 2-subgroup $P_n(2)$ of symmetric group $S_{2^n}$ is a minimal generating set of this subgroup consisting of elements with only one non-zero coordinate in the polynomial representation. For different diagonal bases Cayley graphs of $P_n(2)$ may have different girths (i.e. minimal lengths of cycles) and thus be non-isomorphic. In presented paper all possible values of girths of Cayley graphs of $P_n(2)$ on diagonal bases are calculated. A criterion for whenever such Cayley graph has girth equal to 4 is presented. A lower bound for the number of different non-isomorphic Cayley graphs of $P_n(2)$ on diagonal bases is proposed.

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BibTeX RIS

Bartłomiej Pawlik. 2018-06-22. The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases. https://arxiv.org/abs/1806.08604

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