On Suborbits and Graphs Associated with Action of Alternating Groups on Cartesian Product of Two Sets
Stephen Kadedesya *
Pan African University, Institute for Basic Sciences, Technology and Innovation, Nairobi, Kenya and Busitema University, Tororo, Uganda.
Lewis Nyaga
Jommo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.
Jane Rimberia
Kenyatta University, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the suborbits and graphs associated with the action of direct product of two Alternating groups on the Cartesian product of two sets are studied. It is shown that the suborbits are self-paired and the associated graphs are undirected and regular with girth 3.
Keywords: Alternating group, suborbit, suborbital graph, self-paired, connected component, girth, undirected, direct product, cartesian product