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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 05C25
Secondary: 05C20, 05C40
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Milestones
Received: 26 May 2017
Revised: 26 July 2017
Accepted: 1 August 2017
Published: 15 January 2018
Communicated by Ann N. Trenk
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Authors |
| Patreck Chikwanda | |
| Department of Mathematics and
Statistics Georgia State University Atlanta, GA United States |
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| Cathy Kriloff | |
| Department of Mathematics and
Statistics Idaho State University Pocatello, ID United States |
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| Yun Teck Lee | |
| Idaho State University Pocatello, ID United States |
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| Taylor Sandow | |
| Idaho State University Pocatello, ID United States |
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| Garrett Smith | |
| Idaho State University Pocatello, ID United States |
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| Dmytro Yeroshkin | |
| Idaho State University Pocatello, ID United States |
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