Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2017
Committee Chair or Co-Chairs
Teresa Haynes
Committee Members
Robert B. Gardner, Robert A. Beeler
Abstract
The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number of complementary prisms. Our main results show that γR(GG) takes on a limited number of values in terms of the domination number of GG and the Roman domination numbers of G and G.
Document Type
Thesis - unrestricted
Recommended Citation
Alhashim, Alawi I., "Roman Domination in Complementary Prisms" (2017). Electronic Theses and Dissertations. Paper 3175. https://dc.etsu.edu/etd/3175
Copyright
Copyright by the authors.