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2006 | 26 | 1 | 5-18
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Algorithmic aspects of total-subdomination in graphs

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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.
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  • School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa
  • Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083 USA
  • School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa
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