An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree

Authors:
Johannes H. Hattingh;Ernst J. Joubert
Affiliations:
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083, USA;Department of Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 6
Cited 1

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Abstract

Let G=(V,E) be a graph. A set S@?V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted @c"r(G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is a connected graph of order n and minimum degree @d and not isomorphic to one of nine exceptional graphs, then @c"r(G)@?n-@d+12.