Fault Tolerance and 2-Domination in Certain Interconnection Networks

Lian Chen and Xiujun Zhang

Journal of Mathematics Research, 2019, vol. 11, issue 2, 181-189

Abstract: A graph could be understood as a sensor network, in which the vertices represent the sensors and two vertices are adjacent if and only if the corresponding devices can communicate with each other. For a network G, a 2-dominating function on G is a function f : V(G) → [0, 1] such that each vertex assigned with 0 has at least two neighbors assigned with 1. The weight of f is Σ_u∈V(G) f (u), and the minimum weight over all 2-dominating functions is the 2-domination number of G. The 2-dominating set problem consists of finding the 2-domination number of a graph and it was proposed to model the fault tolerance of a sensor network. In this paper, we determined substantial 2-domination numbers of 2-dimensional meshes, cylinders, tori and hypercubes.

Keywords: fault tolerance; 2-domination; mesh; cylinder; torus (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/jmr/article/download/0/0/38929/39678 (application/pdf)
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/38929 (text/html)

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:ibn:jmrjnl:v:11:y:2019:i:2:p:181

Access Statistics for this article

More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().