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, University of Mohaghegh Ardabili, Ardabil, Iran.

3 Department of Mathematics, Yazd University, Yazd, Iran.



Let G = (V, E) be a simple graph without isolated vertices. A set D ⊂ V is a total [1, 2]-dominating set if for every vertex v ∈ V , 1 ≤ |N(v) ∩ D| ≤ 2. The total [1, 2]-domination problem is to determine the total [1, 2]-domination number γt[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 γt[1,2](G) for a block graph G.


Main Subjects

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