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Discrete Mathematics and Combinatorics
University of Nebraska - Lincoln
Department of Computer Science and Engineering: Dissertations, Theses, and Student Research
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Asteroidal Sets And Dominating Targets In Graphs, Oleksiy Al-Saadi
Asteroidal Sets And Dominating Targets In Graphs, Oleksiy Al-Saadi
Department of Computer Science and Engineering: Dissertations, Theses, and Student Research
The focus of this PhD thesis is on various distance and domination properties in graphs. In particular, we prove strong results about the interactions between asteroidal sets and dominating targets. Our results add to or extend a plethora of results on these properties within the literature. We define the class of strict dominating pair graphs and show structural and algorithmic properties of this class. Notably, we prove that such graphs have diameter 3, 4, or contain an asteroidal quadruple. Then, we design an algorithm to to efficiently recognize chordal hereditary dominating pair graphs. We provide new results that describe the …