Matrix Formulation of EISs of Graphs and Its Application to WSN Covering Problems

Yongyi Yan, Jumei Yue, He Deng and Elena Guardo

Journal of Mathematics, 2021, vol. 2021, 1-12

Abstract: In this paper, the problem of formulating and finding externally independent sets of graphs is considered by using a newly developed STP method, called semitensor product of matrices. By introducing a characteristic value of a vertex subset of a graph and using the algebraic representation of pseudological functions, several necessary and sufficient conditions of matrix form are proposed to express the externally independent sets (EISs), minimum externally independent sets (MEISs), and kernels of graphs. Based on this, the concepts of EIS matrix, MEIS matrix, and kernel matrix are introduced. By these matrices’ complete characterization of these three structures of graphs, three algorithms are further designed which can find all these kinds of subsets of graphs mathematically. The results are finally applied to a WSN covering problem to demonstrate the correctness and effectiveness of the proposed results.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2021/5526532.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2021/5526532.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5526532

DOI: 10.1155/2021/5526532

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().