Open AccessFault Tolerance and 2-Domination in Certain Interconnection Networks
Author(s) -
Lian Chen,
Xiujun Zhang
Publication year - 2019
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v11n2p181
Subject(s) - mathematics , hypercube , combinatorics , domination analysis , vertex (graph theory) , fault tolerance , dominating set , discrete mathematics , interconnection , graph , weight function , minimum weight , computer science , distributed computing , computer network , statistics
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.