On the computational complexity of upper total domination

Authors:
Qizhi Fang
Affiliations:
Department of Mathematics, Ocean University of China, Qingdao 266003, Shandong, China
Venue:
Discrete Applied Mathematics - Discrete mathematics and theoretical computer science (DMTCS)
Year:
2004

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Abstract

Let G = (V, E) be an undirected graph. Upper total domination number Γt(G) is the maximum cardinality over all minimal total dominating sets of G, and upper fractional total domination number rt(G) is the maximum weight over all minimal total dominating functions of G. In this paper we show that: (1) rtt(G) is an optimal value of some linear programming and is always a rational number; (2) when G is a tree, Γt(G) = rt(G); (3) the recognition problems corresponding to the problems of computing Γt(G) and rt(G) are both NP-complete.