Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

5-2006

Committee Chair or Co-Chairs

Teresa W. Haynes

Committee Members

Anant P. Godbole, Debra J. Knisley

Abstract

In a graph G=(V,E), a subset SV is a double dominating set if every vertex in V is dominated at least twice. The minimum cardinality of a double dominating set of G is the double domination number. A graph G is double domination edge critical if for any edge uvE(), the double domination number of G+uv is less than the double domination number of G. We investigate properties of double domination edge critical graphs. In particular, we characterize the double domination edge critical trees and cycles, graphs with double domination numbers of 3, and graphs with double domination numbers of 4 with maximum diameter.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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