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A characterisation of universal minimal total dominating functions in trees

✍ Scribed by E.J. Cockayne; C.M. Mynhardt

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 445 KB
Volume: 141
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0192-7

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✦ Synopsis

A total dominating function (TDF) of a graph G = (V, E) is a function f: V~ [0, 1] such that for each v~ V, ~u~Ntv)f(u)>~ 1, where N(v) denotes the set of neighbours of v. Although convex combinations of TDFs are also TDFs, convex combinations of minimal TDFs (MTDFs) are not necessarily minimal. An MTDF whose convex combinations with any other MTDF are minimal is called a universal MTDF. In this paper we characterise universal MTDFs for trees.

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