Efficient domination through eigenvalues

Cardoso, Domingos M.; Luz, Carlos J.; Pacheco, Maria F.

doi:10.1016/j.dam.2016.06.014

Cited by 3 publications

(7 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Determination of a (0, τ )-regular set of an adverse graph by solving a linear system. The following theorem unifies the results obtained in [11,8] which can be applied for the determination of a (κ, τ )-regular set, with κ = 0 and τ = −λ min (G).…”

Section: 1supporting

confidence: 60%

“…However, in general, it is hard to decide whether the upper bound υ(G) coincides with the stability number α(G) and throughout more than two decades, this has been the main challenge within this topic. This survey starts in Section 2 by relating the convex quadratic program (11) with the Motzkin-Straus quadratic model for the determination of the clique (stability) number of a graph G [31] by the introduction of the parametric quadratic programs (1) and (4) whose optimal values, υ G (τ ) and ν G (τ ), are the inverse of each other and equal to α(G) in the former case (1/α(G) in the later) when τ = 1 (see (8)). Notice that (11) is obtained from (1) by setting τ = −λ min (G).…”

Section: Discussionmentioning

confidence: 99%

“…Theorem 4.4. [11,8] Considering a graph G of order n, let x be a particular solution of the linear system…”

Section: Recognition Of Convex-qp Graphsmentioning

confidence: 99%

See 2 more Smart Citations

A survey on graphs with convex quadratic stability number

Cardoso

2018

Optimization

Self Cite

View full text Add to dashboard Cite

A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound on the stability number was introduced, a necessary and sufficient condition for this upper bound be attained was deduced. The recognition of graphs with convex quadratic stability number has been deeply studied with several consequences from continuous and combinatorial point of view. This survey starts with an exposition of some extensions of the classical Motzkin-Straus approach to the determination of the stability number of a graph and its relations with the convex quadratic programming upper bound. The main advances, including several properties and alternative characterizations of graphs with convex quadratic stability number are described as well as the algorithmic strategies developed for their recognition. Open problems and a conjecture for a particular class of graphs, herein called adverse graphs, are presented, pointing out a research line which is a challenge between continuous and discrete problems.2010 Mathematics Subject Classification. 90C20, 90C35, 05C69, 05C50. Key words and phrases. convex quadratic programming in graphs; stability number of graphs; relations between continuous and discrete optimization.

show abstract

Section: 1supporting

confidence: 60%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A survey on graphs with convex quadratic stability number

Cardoso

2018

Optimization

Self Cite

View full text Add to dashboard Cite

show abstract

“…The fourth one explains 7.62%, which is only 44.84% of the inertia clarified by the previous dimension. Because the first three dimensions provide a 77.59% share of the data inertia together, we can set the number of statistically significant dimensions to three [ 31 ]. It means the three strongest self-governing regions – in terms of the strength from an angle of view of this analysis – are able to perform as the whole dataset.…”

Section: Resultsmentioning

confidence: 99%

Regional disparities in medical equipment distribution in the Slovak Republic – a platform for a health policy regulatory mechanism

2017

View full text Add to dashboard Cite

BackgroundThis study aims to examine the localisation of selected parameters in the deployment and use of medical equipment in the Slovak Republic and to verify potential regional disparities. The study evaluates the benefits of an analytical platform for regulatory mechanisms in the healthcare system.MethodsThe correspondence analysis is applied to the entire data set containing information regarding medical equipment distribution and mortality.ResultsThe results highlight regional differences in the use of medical equipment throughout the analysed period from 2008 to 2014. The total amount of medical equipment increased slightly to 9192 devices during the time span. In 2014, there was a significant decrease of 16.44%. Disparities are found in the frequencies and structure of medical equipment. In some regions, medical equipment is not present or is present in low numbers.ConclusionsThe results regarding regional disparities demonstrate the regional development of the amount of medical equipment. The deployment of medical equipment is not proportional, and not all of the analysed devices are available in each region. The tests also indicate the appropriateness of the amount of medical equipment and create a platform for further investigation. The results of the analysis suggest the unsuitable distribution of medical equipment throughout the Slovak regions, where there are significant regional disparities. These findings can serve as a monitoring platform to evaluate the accessibility and efficiency of medical equipment usage.Trial registrationNo human participants were involved in the research.

show abstract

“…Corollary 3.2. [12] If a graph G has a (κ, τ )-regular set S ⊆ V (G) and x is a particular solution of the linear system (1.1), then |S| = êT x.…”

Section: Determination Of (κ τ )-Regular Setsmentioning

confidence: 99%