Connectedness of two-sided group digraphs and graphs
Combinatorics
2018-04-04 v3 Group Theory
Abstract
Two-sided group digraphs and graphs, introduced by Iradmusa and Praeger, provide a generalization of Cayley digraphs and graphs in which arcs are determined by left and right multiplying by elements of two subsets of the group. We characterize when two-sided group digraphs and graphs are weakly and strongly connected and count connected components, using both an explicit elementary perspective and group actions. Our results and examples address four open problems posed by Iradmusa and Praeger that concern connectedness and valency. We pose five new open problems.
Keywords
Cite
@article{arxiv.1705.05827,
title = {Connectedness of two-sided group digraphs and graphs},
author = {Patreck Chikwanda and Cathy Kriloff and Yun Teck Lee and Taylor Sandow and Garrett Smith and Dmytro Yeroshkin},
journal= {arXiv preprint arXiv:1705.05827},
year = {2018}
}
Comments
Made changes suggested by referee. Added five new open problems. To appear in Involve