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