The Domination Number of Kα□Kb□Kc

Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Allen Schwenk

Second Advisor

Dr. Annegret Paul

Third Advisor

Dr. Andrzej Dudek

Fourth Advisor

Dr. Linda Lesniak


A subset S of a graph G = (V,E) is said to be a dominating set if each vertex of V is either in the set S or is adjacent to at least one vertex in S. The minimum cardinality among the dominating sets of G is called the domination number of G and is denoted by ϒ(G). Historically, the domination number is one of the most popular topics in graph theory. It is known that finding the domination number of a given graph G is NP hard. In this thesis, we consider the domination number of Cartesian products of complete graphs.

[The rest of the abstract contains formulas that can be viewed in the dissertation itself.]


A print copy can be found in Waldo Library at call number QA 9999.2.L56 and can be requested through Interlibrary Loan.

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