On the computational complexity of Roman{2}-domination in grid graphs

被引:0
|
作者
Amouzandeh, Aflatoun [1 ]
Moradi, Ahmad [2 ]
机构
[1] Univ Siegen, Dept Math, Siegen, Germany
[2] Univ Mazandaran, Dept Math Sci, Babolsar, Iran
关键词
Computational complexity; Roman{2}-domination; APX-hardness; Grid graphs; DOMINATION;
D O I
10.1007/s10878-023-01024-7
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A Roman{2}-dominating function of a graph G = (V, E) is a function f : V ? {0, 1, 2} such that every vertex x ? V with f (x) = 0 either there exists at least one vertex y ? N(x) with f (y) = 2 or there are at least two vertices u, v ? N(x) with f (u) = f (v) = 1. The weight of a Roman{2}-dominating function f on G is defined to be the value of S-x?V f (x). The minimum weight of a Roman{2}-dominating function on G is called the Roman{2}-domination number of G. In this paper, we prove that the decision problem associated with Roman{2}-domination number is N P-complete even when restricted to subgraphs of grid graphs. Additionally, we answer an open question about the approximation hardness of Roman{2}-domination problem for bounded degree graphs.
引用
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页数:10
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