Perfect Italian domination in graphs: Complexity and algorithms
An Italian dominating function on a simple undirected graph G is a function f:V(G)⟶{0,1,2} satisfying the condition that for each vertex v with f(v)=0, ∑u∈NG(v)f(u)≥2. An Italian dominating function f on G is called a perfect Italian dominating function on G if for each vertex v with f(v)=0, ∑u∈NG(v...
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| Vydáno v: | Discrete Applied Mathematics Ročník 319; s. 271 - 295 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
15.10.2022
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | An Italian dominating function on a simple undirected graph G is a function f:V(G)⟶{0,1,2} satisfying the condition that for each vertex v with f(v)=0, ∑u∈NG(v)f(u)≥2. An Italian dominating function f on G is called a perfect Italian dominating function on G if for each vertex v with f(v)=0, ∑u∈NG(v)f(u)=2. The weight of a function f on a graph G, denoted by w(f), is the sum ∑v∈V(G)f(v). For a simple undirected graph G, Min-PIDF is the problem of finding the minimum weight of a perfect Italian dominating function on G. First, we discuss the complexity difference between Min-PIDF and the problem of finding the minimum weight of an Italian dominating function. We then establish the NP-completeness of the decision version of Min-PIDF in chordal graphs and investigate the hardness of approximation of Min-PIDF in general graphs. Finally, we present linear time algorithms for computing the minimum weight of a perfect Italian dominating function in block graphs and series-parallel graphs. |
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| AbstractList | An Italian dominating function on a simple undirected graph G is a function f:V(G)⟶{0,1,2} satisfying the condition that for each vertex v with f(v)=0, ∑u∈NG(v)f(u)≥2. An Italian dominating function f on G is called a perfect Italian dominating function on G if for each vertex v with f(v)=0, ∑u∈NG(v)f(u)=2. The weight of a function f on a graph G, denoted by w(f), is the sum ∑v∈V(G)f(v). For a simple undirected graph G, Min-PIDF is the problem of finding the minimum weight of a perfect Italian dominating function on G. First, we discuss the complexity difference between Min-PIDF and the problem of finding the minimum weight of an Italian dominating function. We then establish the NP-completeness of the decision version of Min-PIDF in chordal graphs and investigate the hardness of approximation of Min-PIDF in general graphs. Finally, we present linear time algorithms for computing the minimum weight of a perfect Italian dominating function in block graphs and series-parallel graphs. |
| Author | Pradhan, D. Liu, Jia-Bao Banerjee, S. |
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| Keywords | Domination NP-complete Italian domination Polynomial time algorithm Perfect Italian domination |
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