A factoring of a graph G = (V,E) is a collection of spanning subgraphs F1, F2, ?, Fk, known as factors into which the edge set E has been partitioned. A dominating set of a graph is a set of nodes such that every node in the graph is either contained in the set or has an edge to some node in the set. Each factor Fi is itself a graph and so has a dominating set. This set is called a local dominating set or LDS. An LDS of minimum size contains (gamma)i nodes. In addition, there is some set of nodes named a global dominating set which dominates all of the factors. If a global dominating set is of a minimum size, it is called a GDS and contains (gamma) nodes. A central question answered by this dissertation is under what circumstances, given a set of integers (gamma)1, (gamma)2, ..., (gamma)k, and (gamma) there is a graph which can be factored into k factors in such a way that a minimum LDS of Fi has size (gamma)i, 1 < = i < = k, and GDS has size (gamma).
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Brooks, George H.
Doctor of Philosophy (Ph.D.)
College of Arts and Sciences
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Doctoral Dissertation (Open Access)
Carrington, Julie R., "Global domination of factors of a graph" (1992). Retrospective Theses and Dissertations. 4389.