# Some Sharp Bounds on the Negative Decision Number of Graphs

• Volume: 33, Issue: 4, page 649-656
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Hongyu Liang. "Some Sharp Bounds on the Negative Decision Number of Graphs." Discussiones Mathematicae Graph Theory 33.4 (2013): 649-656. <http://eudml.org/doc/267662>.

@article{HongyuLiang2013,
abstract = {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.},
author = {Hongyu Liang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {negative decision number; bad function; sharp upper bounds; Nordhaus-Gaddum results},
language = {eng},
number = {4},
pages = {649-656},
title = {Some Sharp Bounds on the Negative Decision Number of Graphs},
url = {http://eudml.org/doc/267662},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Hongyu Liang
TI - Some Sharp Bounds on the Negative Decision Number of Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 4
SP - 649
EP - 656
AB - 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.
LA - eng
KW - negative decision number; bad function; sharp upper bounds; Nordhaus-Gaddum results
UR - http://eudml.org/doc/267662
ER -

## References

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