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Some results on universal minimal total dominating functions

โœ Scribed by Fang Qizhi; Cai Maocheng


Book ID
110611679
Publisher
Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2001
Tongue
English
Weight
485 KB
Volume
17
Category
Article
ISSN
0168-9673

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We show that any tree that has a universal minimal total dominating function has one which only takes 0-1 values. K 3 demonstrates that this fails for graphs in general. Given a graph G =(V, E), for each vertex ve V let F(v) be the set of its neighbours (in particular, not including v itself). A to

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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

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A total dominating function (TDF) of a graph G = (V, E) is a function f : V โ†’ [0, 1] such that for each v โˆˆ V , the sum of f values over the open neighbourhood of v is at least one. Zero-one valued TDFs are precisely the characteristic functions of total dominating sets of G. We study the convexity

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## Abstract A total dominating function (TDF) of a graph __G__ = (__V, E__) is a function __f__: __V__ โ† [0, 1] such that for each __v__ ฯต V, ฮฃ~uฯตN(v)~ f(u) โ‰ฅ 1 (where __N__(__v__) denotes the set of neighbors of vertex __v__). Convex combinations of TDFs are also TDFs. However, convex combinations