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

Connectedness of two-sided group digraphs and graphs. (English) Zbl 1390.05087

Involve 11, No. 4, 679-699 (2018).
Summary: Two-sided group digraphs and graphs, introduced by M. N. Iradmusa and C. E. Praeger [J. Graph Theory 82, No. 3, 279–295 (2016; Zbl 1342.05062)], 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.

Cited in 1 Document

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C20 Directed graphs (digraphs), tournaments
05C40 Connectivity

Keywords:

two-sided group digraph; Cayley graph; group; connectivity

Citations:

Zbl 1342.05062
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\textit{P. Chikwanda} et al., Involve 11, No. 4, 679--699 (2018; Zbl 1390.05087)
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