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On the computational complexity of upper total domination

✍ Scribed by Qizhi Fang

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
359 KB
Volume
136
Category
Article
ISSN
0166-218X

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✦ Synopsis

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

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