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NOTE ON THE NEGATIVE DECISION NUMBER IN DIGRAPHS

  • Kim, Hye Kyung (Department of Mathematics Education, Catholic University of Daegu)
  • Received : 2013.06.06
  • Accepted : 2014.05.20
  • Published : 2014.05.31

Abstract

Let D be a finite digraph with the vertex set V (D) and the arc set A(D). A function f : $V(D){\rightarrow}\{-1,\;1\}$ defined on the vertices of a digraph D is called a bad function if $f(N^-(v)){\leq}1$ for every v in D. The weight of a bad function is $f(V(D))=\sum\limits_{v{\in}V(D)}f(v)$. The maximum weight of a bad function of D is the the negative decision number ${\beta}_D(D)$ of D. Wang [4] studied several sharp upper bounds of this number for an undirected graph. In this paper, we study sharp upper bounds of the negative decision number ${\beta}_D(D)$ of for a digraph D.

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References

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