Discussiones Mathematicae Graph Theory 26(1) (2006) 5-18
doi: 10.7151/dmgt.1296

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ALGORITHMIC ASPECTS OF TOTAL-SUBDOMINATION IN GRAPHS

1Laura M. Harris, 2Johannes H. Hattingh and 1Michael A. Henning

1School of Mathematical Sciences
University of KwaZulu-Natal
Pietermaritzburg, 3209 South Africa

2Department of Mathematics and Statistics
Georgia State University
Atlanta, GA 30303-3083 USA
e-mail: jhhattingh@gsu.edu

Abstract

Let G = (V,E) be a graph and let k ∈ Z+. A total k-subdominating function is a function f: V → {−1,1} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f(V) over all total k-subdominating functions f of G where f(V) denotes the sum of the function values assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination number of a tree and also show that the associated decision problem is NP-complete for general graphs.

Keywords: total k-subdomination, algorithm, tree.

2000 Mathematics Subject Classification: 05C69.

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Received 15 September 2003
Revised 24 August 2005