Power Domination Problem in Graphs

2005 ◽  
pp. 818-828 ◽  
Author(s):  
Chung-Shou Liao ◽  
Der-Tsai Lee
Keyword(s):  
Power Domination ◽  
Domination Problem

The k-power domination problem in weighted trees

2020 ◽  
Vol 809 ◽  
pp. 231-238
Author(s):  
Changjie Cheng ◽  
Changhong Lu ◽  
Yu Zhou
Keyword(s):  
Power Domination ◽  
Weighted Trees ◽  
Domination Problem

Minimizing Missed Opportunities: Modeling Relationships between the State and Business in Russia

2009 ◽  
pp. 42-61
Author(s):  
A. Oleynik
Keyword(s):  
Decision Making ◽  
Empirical Evidence ◽  
Common Good ◽  
The State ◽  
Power Relationships ◽  
Individual Decision ◽  
Missed Opportunities ◽  
Power Domination ◽  
Individual Decision Making ◽  
Optimal Outcomes

Power involves a number of models of choice: maximizing, satisficing, coercion, and minimizing missed opportunities. The latter is explored in detail and linked to a particular type of power, domination by virtue of a constellation of interests. It is shown that domination by virtue of a constellation of interests calls for justification through references to a common good, i.e. a rent to be shared between Principal and Agent. Two sources of sub-optimal outcomes are compared: individual decision-making and interactions. Interactions organized in the form of power relationships lead to sub-optimal outcomes for at least one side, Agent. Some empirical evidence from Russia is provided for illustrative purposes.

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.

Disproofs of three conjectures on the power domination of graphs

2022 ◽  
Vol 307 ◽  
pp. 62-64
Author(s):  
Wei Yang ◽  
Baoyindureng Wu
Keyword(s):  
Power Domination

k-Efficient domination: Algorithmic perspective

2022 ◽  
Author(s):  
Mohsen Alambardar Meybodi
Keyword(s):  
Decision Problem ◽  
Dominating Set ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Chordal Graphs ◽  
Sparse Graphs ◽  
Fpt Algorithm ◽  
Domination Problem ◽  
Efficient Dominating Set ◽  
Np Complete

A set [Formula: see text] of a graph [Formula: see text] is called an efficient dominating set of [Formula: see text] if every vertex [Formula: see text] has exactly one neighbor in [Formula: see text], in other words, the vertex set [Formula: see text] is partitioned to some circles with radius one such that the vertices in [Formula: see text] are the centers of partitions. A generalization of this concept, introduced by Chellali et al. [k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122], is called [Formula: see text]-efficient dominating set that briefly partitions the vertices of graph with different radiuses. It leads to a partition set [Formula: see text] such that each [Formula: see text] consists a center vertex [Formula: see text] and all the vertices in distance [Formula: see text], where [Formula: see text]. In other words, there exist the dominators with various dominating powers. The problem of finding minimum set [Formula: see text] is called the minimum [Formula: see text]-efficient domination problem. Given a positive integer [Formula: see text] and a graph [Formula: see text], the [Formula: see text]-efficient Domination Decision problem is to decide whether [Formula: see text] has a [Formula: see text]-efficient dominating set of cardinality at most [Formula: see text]. The [Formula: see text]-efficient Domination Decision problem is known to be NP-complete even for bipartite graphs [M. Chellali, T. W. Haynes and S. Hedetniemi, k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122]. Clearly, every graph has a [Formula: see text]-efficient dominating set but it is not correct for efficient dominating set. In this paper, we study the following: [Formula: see text]-efficient domination problem set is NP-complete even in chordal graphs. A polynomial-time algorithm for [Formula: see text]-efficient domination in trees. [Formula: see text]-efficient domination on sparse graphs from the parametrized complexity perspective. In particular, we show that it is [Formula: see text]-hard on d-degenerate graphs while the original dominating set has Fixed Parameter Tractable (FPT) algorithm on d-degenerate graphs. [Formula: see text]-efficient domination on nowhere-dense graphs is FPT.

scholarly journals HONG KONG SAR IMMIGRATION IN THE DYNAMICS OF POLITICS, POLICY AND INSTITUTION

2018 ◽  
Vol 1 (2) ◽  
pp. 69-81
Author(s):  
Andry Indrady
Keyword(s):  
Hong Kong ◽  
Transition Period ◽  
Executive Power ◽  
Power Domination ◽  
The Public ◽  
Hong Kong Sar ◽  
British Colonial ◽  
The Government ◽  
Colonial Government ◽  
And Control

The Bureaucratic System of the Immigration Department of Hong Kong SAR is one of the legacies from British Colonial Government seen from legal and also immigration bureaucratic perspectives reflect the executive power domination over immigration policymaking. This is understandable since Hong Kong SAR adopts “Administrative State Model” which means Immigration Officer as a bureaucrat holds significant roles at both stages of policymaking and also its implementation. This research looks at transition period of the Immigration Department and its policies since the period of handover of Hong Kong SAR from the British Government to the Government of China especially throughout the concern from the public including academics about the future of immigration policies made by the Department that arguably from colonial to current being used as political and control tools to safeguard the interest of the Ruler. This situation ultimately will question the existence of Hong Kong SAR as one of the International Hub in the Era of Millennium.  

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