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

Adrian Michalski, Iwona Włoch
2020 Applied Mathematics and Computation  
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 N P -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
more » ... al factors using Padovan and Perrin numbers.
doi:10.1016/j.amc.2020.125155 fatcat:x6uydi5zqjfuzd7rmdurgjukhu