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2018 Connectedness of two-sided group digraphs and graphs
Patreck Chikwanda, Cathy Kriloff, Yun Teck Lee, Taylor Sandow, Garrett Smith, Dmytro Yeroshkin
Involve 11(4): 679-699 (2018). DOI: 10.2140/involve.2018.11.679

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.

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Patreck Chikwanda. Cathy Kriloff. Yun Teck Lee. Taylor Sandow. Garrett Smith. Dmytro Yeroshkin. "Connectedness of two-sided group digraphs and graphs." Involve 11 (4) 679 - 699, 2018. https://doi.org/10.2140/involve.2018.11.679

Information

Received: 26 May 2017; Revised: 26 July 2017; Accepted: 1 August 2017; Published: 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06864403
MathSciNet: MR3778919
Digital Object Identifier: 10.2140/involve.2018.11.679

Subjects:
Primary: 05C25
Secondary: 05C20‎ , 05C40

Keywords: Cayley graph , connectivity , group , two-sided group digraph

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2018
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