This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of …
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Most interesting optimization problems on graphs are NP-hard, implying that (unless P=NP) there is no polynomial time algorithm that solves all the instances of an NP-hard problem exactly. However, classical complexity measures the running time as a function of only the overall …
In this thesis we discuss two topics: domination parameters and inducibility. In the first chapter, we introduce basic concepts, definitions, and a brief history for both types of problems. We will first inspect domination parameters in graphs, particularly independent dominatio…