Enumeration of dicirculant digraphs
Jing Wang, Ligong Wang, Xiaogang Liu

TL;DR
This paper counts the number of dicirculant digraphs over the dicyclic group of order 4p, using Pólya's Enumeration Theorem, including connected graphs and those with specified out-degree.
Contribution
It provides a complete enumeration of dicirculant digraphs of order 4p, including connected cases and fixed out-degree, which was not previously known.
Findings
Number of dicirculant digraphs up to isomorphism calculated
Enumeration includes connected and out-degree specific graphs
Utilizes Pólya Enumeration Theorem for counting
Abstract
Let be the dicyclic group of order . A Cayley digraph over is called a dicirculant digraph. In this paper, we calculate the number of (connected) dicirculant digraphs of order ( prime) up to isomorphism by using the P\'olya Enumeration Theorem. Moreover, we get the number of (connected) dicirculant digraphs of order ( prime) and out-degree for every .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Graph Theory Research
