Baskınlık sayısının versiyonları ve bunların rassal aralık yakalama yönlü çizge aileleri üzerinde dağılımları

In this thesis we provide some extensions of the concept of domination in graph theory, namely, exact p-domination, weak p-domination and strong p-domination. We illustrate these new concepts on some random families of geometric graphs called class cover catch digraphs (CCCDs) and proximity catch digraphs (PCDs). PCDs and CCCDs are closely related to each other and have applications in pattern classication and spatial point pattern analysis. Furthermore, PCDs are parameterized by an expansion parameter and a centrality parameter. Previously, usual domination has been investigated thoroughly for these digraph families. We investigate the distribution of various extensions of domination number for these digraph families. In particular, we demonstrate that the asymptotic distribution of strong p-domination number is degenerate for CCCDs. We also derive the asymptotic distribution of the various domination number concepts for PCDs based on one dimensional uniform data. We also perform Monte Carlo simulation experiments, which support our theoretical ndings. This study lays the foundation for the study of the various forms of domination on PCDs based on higher dimensional data.