scholarly journals Complexity of distance paired-domination problem in graphs

2012 ◽  
Vol 459 ◽  
pp. 89-99 ◽  
Author(s):  
Gerard J. Chang ◽  
B.S. Panda ◽  
D. Pradhan
Keyword(s):  
Domination Problem ◽  
Paired Domination

Paired-Domination Problem on Distance-Hereditary Graphs

Algorithmica ◽  
2020 ◽  
Vol 82 (10) ◽  
pp. 2809-2840
Author(s):  
Ching-Chi Lin ◽  
Keng-Chu Ku ◽  
Chan-Hung Hsu
Keyword(s):  
Domination Problem ◽  
Paired Domination

scholarly journals AnO(n)-time algorithm for the paired domination problem on permutation graphs

2013 ◽  
Vol 34 (3) ◽  
pp. 593-608 ◽  
Author(s):  
Evaggelos Lappas ◽  
Stavros D. Nikolopoulos ◽  
Leonidas Palios
Keyword(s):  
Time Algorithm ◽  
Permutation Graphs ◽  
Domination Problem ◽  
Paired Domination

scholarly journals A Note on the Paired-Domination Subdivision Number of Trees

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 181 ◽  
Author(s):  
Xiaoli Qiang ◽  
Saeed Kosari ◽  
Zehui Shao ◽  
Seyed Mahmoud Sheikholeslami ◽  
Mustapha Chellali ◽  
...  
Keyword(s):  
Upper Bound ◽  
Isolated Vertex ◽  
Paired Domination ◽  
Domination Subdivision Number

For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star), then sdγpr(T)≤min{γpr(T)2+1,n2}, improving the (n−1)-upper bound that was recently proven.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

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