Efficient Minus Domination Problem on Block Graphs

• Main Authors: Yung-Li Chang, 張永立
• Other Authors: Maw-Shang Chang
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/51308210507211991009

碩士 === 國立中正大學 === 資訊工程研究所 === 91 === A three-valued function $f$ defined on the vertices of a graph $G = (V, E)$, $f : V \rightarrow \{-1, 0, 1\}$, is an efficient minus dominating function if the sum of its function values over any closed neighborhood equals to one. That is, for every $v \in V$, $\sum_{u \in N[v]}f(u) = 1$, where $N[v]$ consists of $v$ and all vertices adjacent to $v$. The sum of the function values of all vertices is called the weight of $f$. The efficient minus domination problem is to find the efficient minus dominating function of $G$ of minimum weight. This problem is NP-complete for general graphs. In this paper, we present an $O(\Delta^4 n)$ algorithm to solve this problem on block graphs where $\Delta$ is the maximum degree of $G$.