Note on The Negative Decision Number in Digraphs
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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 onthe vertices of a digraph $D$ is called a badfunction if $f(N^-(v))\leq 1$ for every $v$ in $D$. The weight of abad function is $f(V(D))=\underset{v\inV(D)}{\sum} f(v)$. The maximum weight of a bad function of $D$ is thethe negative decision number $\beta_D(D)$ of $D$. Wang \cite{w} studiedseveral sharp upper bounds of this number for a undirected graph. In this paper, we study sharp upper bounds of the negative decision number $\beta_D(D)$ of fora digraph $D$.
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 onthe vertices of a digraph $D$ is called a badfunction if $f(N^-(v))\leq 1$ for every $v$ in $D$. The weight of abad function is $f(V(D))=\underset{v\inV(D)}{\sum} f(v)$. The maximum weight of a bad function of $D$ is thethe negative decision number $\beta_D(D)$ of $D$. Wang \cite{w} studiedseveral sharp upper bounds of this number for a undirected graph. In this paper, we study sharp upper bounds of the negative decision number $\beta_D(D)$ of fora digraph $D$.
참고문헌 (5)
- G. Chartrand, "Graphs and digraphs" (2000), Chapman and Hall
- M.A. Henning, "Signed 2-independence in graphs", Discrete Math, 250, pp.93~107 (2002)
- L. Volkmann, "Signed 2-independence in digraphs", Discrete. Math, 312, pp.465~471 (2012)
- C. Wang, "The negative decision number in graphs", Australasian J. of Combinatorics, 41, pp.263~272 (2008)
- B. Zelinka, "On signed 2-independence numbers of graphs", ~