On the Independence Number of Cayley Digraphs of Rectangular Groups

Abstract

© 2018, Springer Japan KK, part of Springer Nature. A rectangular group is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. Some special cases of rectangular groups consisting of left groups and right groups are also considered here. Let Cay (S, A) denote the Cayley digraph of the rectangular group S with the connection set A. In this paper, we are interested in studying some properties of Cay (S, A) such as the independence, weakly independence, path independence, and weakly path independence. Furthermore, the independence numbers for those properties of Cay (S, A) are also determined.