Roman Domination in Complementary Prisms
Document Type
Article
Publication Date
1-1-2017
Description
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 matching 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.
Citation Information
Alhashim, Alawi; Desormeaux, Wyatt J.; and Haynes, Teresa W.. 2017. Roman Domination in Complementary Prisms. Australasian Journal of Combinatorics. Vol.68(2). 218-228. https://ajc.maths.uq.edu.au/pdf/68/ajc_v68_p218.pdf ISSN: 1034-4942