Independent Perfect Secure Domination in Graphs - Thomas, Merlin; Cynthia, V. Jude Annie (Communications in Mathematics and Applications, 2025)
For a graph \(G=(V,E)\), a subset \(YV\) will be a dominating set if each vertex \(yVY\) possesses a neighbour in \(Y\). A perfect secure dominating set of \(G\) is a dominating set in which every vertex \(yVY\), has a unique vertex \(xY\) such that \(xyE\) and \((Y{x}){y}\) is a dominating set. In addition, if \(Y\) is an independent set, then \(Y\) is an independent perfect secure dominating set of \(G\). We have introduced the concept of independent perfect secure domination, presented the fundamental properties of this new parameter and investigated the independent perfect secure domination in certain classes of graphs such as the connected split graphs and the spiders in this paper. The complexity of the parameter is also discussed.