Some Sharp Bounds on the Negative Decision Number of Graphs

• Autorzy: Hongyu Liang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

negative decision number; bad function; sharp upper bounds; Nordhaus-Gaddum results

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 4
• Strony: 649-656

Daty

wydano

2013-09-01

online

2013-10-15

Twórcy

autor

Hongyu Liang

• Institute for Interdisciplinary Information Sciences Tsinghua University Beijing, China, 100084

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1683