Let G = (V,E) be a graph. A function f : V → {-1,1} is called a bad function of G if ∑u∈NG(v) f(u) ≤ 1 for all v ∈ V where NG(v) denotes the set of neighbors of v in G. The negative decision number of G, introduced in [12], is the maximum value of ∑v∈V f(v) taken over all bad functions of G. In this paper, we present sharp upper bounds on the negative decision number of a graph in terms of its order, minimum degree, and maximum degree. We also establish a sharp Nordhaus-Gaddum-type inequality for the negative decision number.
@article{bwmeta1.element.doi-10_7151_dmgt_1683,
author = {Hongyu Liang},
title = {Some Sharp Bounds on the Negative Decision Number of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {649-656},
zbl = {1295.05177},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1683}
}
Hongyu Liang. Some Sharp Bounds on the Negative Decision Number of Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 649-656. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1683/
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