On the existence and the number of independent (1,2)-dominating sets in the G-join of graphs

Abstract

In 2008 Hedetniemi et al. introduced the concept of secondary dominating sets and pointed out that the problem of the existence of an independent (1,2)-set is NP-complete in the general case. In this paper we study independent (1,2)-dominating sets in certain classes of graphs. We give the complete characterization of G-join of graphs with an independent (1,2)-dominating set. Moreover, we determine the number of all independent (1,2)-dominating sets in the G-join of special factors using Padovan and Perrin numbers.