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


Domination number, Catesian product, complete graph, independent domination number


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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