Vol. 11, No. 4, 2018

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Connectedness of two-sided group digraphs and graphs

Patreck Chikwanda, Cathy Kriloff, Yun Teck Lee, Taylor Sandow, Garrett Smith and Dmytro Yeroshkin

Vol. 11 (2018), No. 4, 679–699
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
two-sided group digraph, Cayley graph, group, connectivity
Mathematical Subject Classification 2010
Primary: 05C25
Secondary: 05C20, 05C40
Milestones
Received: 26 May 2017
Revised: 26 July 2017
Accepted: 1 August 2017
Published: 15 January 2018

Communicated by Ann N. Trenk
Authors
Patreck Chikwanda
Department of Mathematics and Statistics
Georgia State University
Atlanta, GA
United States
Cathy Kriloff
Department of Mathematics and Statistics
Idaho State University
Pocatello, ID
United States
Yun Teck Lee
Idaho State University
Pocatello, ID
United States
Taylor Sandow
Idaho State University
Pocatello, ID
United States
Garrett Smith
Idaho State University
Pocatello, ID
United States
Dmytro Yeroshkin
Idaho State University
Pocatello, ID
United States