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CONVEXITY OF MINIMAL DOMINATING FUNCTIONS OF TREES: A SURVEY

โœ Scribed by Cockayne, E. J.; Mynhardt, C. M.

Book ID
118175300
Publisher
Taylor and Francis Group
Year
1993
Tongue
English
Weight
743 KB
Volume
16
Category
Article
ISSN
1607-3606

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The relation Ye on the set of minimal dominating functions (MDFs) of a finite graph G is defined by f&?g if and only if any convex combination off and g is also an MDF. If fis a nonintegral MDF of a tree, the existence of another MDF with fewer nonintegral values and other desirable properties is es

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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

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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