Enumeration of dicirculant digraphs

Fuente: arXiv
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Main Authors: Wang, Jing, Wang, Ligong, Liu, Xiaogang
Format: Preprint
Published: 2024
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author Wang, Jing
Wang, Ligong
Liu, Xiaogang
author_facet Wang, Jing
Wang, Ligong
Liu, Xiaogang
contents Let $T_{4p}=\langle a,b\mid a^{2p}=1,a^p=b^2, b^{-1}ab=a^{-1}\rangle$ be the dicyclic group of order $4p$. A Cayley digraph over $T_{4p}$ is called a dicirculant digraph. In this paper, we calculate the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) up to isomorphism by using the Pólya Enumeration Theorem. Moreover, we get the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) and out-degree $k$ for every $k$.
format Preprint
id arxiv_https___arxiv_org_abs_2409_04695
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Enumeration of dicirculant digraphs
Wang, Jing
Wang, Ligong
Liu, Xiaogang
Combinatorics
Let $T_{4p}=\langle a,b\mid a^{2p}=1,a^p=b^2, b^{-1}ab=a^{-1}\rangle$ be the dicyclic group of order $4p$. A Cayley digraph over $T_{4p}$ is called a dicirculant digraph. In this paper, we calculate the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) up to isomorphism by using the Pólya Enumeration Theorem. Moreover, we get the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) and out-degree $k$ for every $k$.
title Enumeration of dicirculant digraphs
topic Combinatorics
url https://arxiv.org/abs/2409.04695