# Some Sharp Bounds on the Negative Decision Number of Graphs

Discussiones Mathematicae Graph Theory (2013)

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

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topHongyu 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 -

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