Independent domination number in Cayley digraphs of rectangular groups

Abstract

© 2018 World Scientific Publishing Company. Let Cay(S,A) denote the Cayley digraph of the rectangular group S with respect to the connection set A in which the rectangular group S is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. An independent dominating set of Cay(S,A) is the independent set of elements in S that can dominate the whole elements. in this paper, we investigate the independent domination number of Cay(S,A) and give more results on Cayley digraphs of left groups and right groups which are specific cases of rectangular groups. Moreover, some results of the path independent domination number of Cay(S,A) are also shown.