A linear-time algorithm to compute total $[1,2]$-domination number of block graphs

Document Type : Original Article


1 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

2 Department of Computer Science, Yazd University, Yazd, Iran

3 Department of Computer Science, University of Mohaghegh Ardabili, Ardabil, Iran

4 Department of Mathematics, Yazd University, Yazd, Iran


Let $G=(V, E)$ be a simple graph without isolated vertices. A set $D\subseteq V$ is a total $[1,2]$-dominating set if for every vertex $v\in V , 1\leq |N(v)\cap D|\leq 2$. The total $[1,2]$-domination problem is to determine the total $[1,2]$-domination number $\gamma_{t[1,2]}(G)$, which is the minimum cardinality of a total $[1,2]$-dominating set for a graph $G$. In this paper, we present a linear-time algorithm to compute $\gamma_{t[1,2]}(G)$, for a block graph $G$.


Main Subjects

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