NOTE ON THE NEGATIVE DECISION NUMBER IN DIGRAPHS

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The negative decision number in graphs

A bad function is a function f : V (G) → {−1, 1} satisfying ∑ v∈N(v) f(v) ≤ 1 for every v ∈ V (G), where N(v) = {u ∈ V (G) | uv ∈ E(G)}. The maximum of the values of ∑ v∈V (G) f(v), taken over all bad functions f, is called the negative decision number and is denoted by βD(G). In this paper, several sharp upper bounds of this number for general graphs are presented.

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ژورنال

عنوان ژورنال: East Asian mathematical journal

سال: 2014

ISSN: 1226-6973

DOI: 10.7858/eamj.2014.025