Enumeration of dicirculant digraphs

Jing Wang; Ligong Wang; Xiaogang Liu

doi:10.1007/s10801-026-01503-0

Enumeration of dicirculant digraphs

Jing Wang
, Ligong Wang
, Xiaogang Liu

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

Abstract

Let T4p=⟨a,b∣a2p=1,ap=b2,b-1ab=a-1⟩ be the dicyclic group of order 4p. A Cayley digraph over T4p 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.

Original language	English
Article number	44
Journal	Journal of Algebraic Combinatorics
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s10801-026-01503-0
State	Published - May 2026

Keywords

Cayley digraph
Cayley isomorphism
dicyclic group

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10.1007/s10801-026-01503-0

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abstract = "Let T4p=⟨a,b∣a2p=1,ap=b2,b-1ab=a-1⟩ be the dicyclic group of order 4p. A Cayley digraph over T4p 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 P{\'o}lya Enumeration Theorem. Moreover, we get the number of (connected) dicirculant digraphs of order 4p (p prime) and out-degree k for every k.",

keywords = "Cayley digraph, Cayley isomorphism, dicyclic group",

author = "Jing Wang and Ligong Wang and Xiaogang Liu",

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T1 - Enumeration of dicirculant digraphs

AU - Wang, Jing

AU - Wang, Ligong

AU - Liu, Xiaogang

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

PY - 2026/5

Y1 - 2026/5

N2 - Let T4p=⟨a,b∣a2p=1,ap=b2,b-1ab=a-1⟩ be the dicyclic group of order 4p. A Cayley digraph over T4p 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.

AB - Let T4p=⟨a,b∣a2p=1,ap=b2,b-1ab=a-1⟩ be the dicyclic group of order 4p. A Cayley digraph over T4p 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.

KW - Cayley digraph

KW - Cayley isomorphism

KW - dicyclic group

UR - https://www.scopus.com/pages/publications/105038076940

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DO - 10.1007/s10801-026-01503-0

M3 - 文章

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SN - 0925-9899

VL - 63

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 3

M1 - 44

ER -

Enumeration of dicirculant digraphs

Abstract

Keywords

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