%0 Journal Article
%T Fault Tolerance and 2-Domination in Certain Interconnection Networks | Chen | Journal of Mathematics Research | CCSE
%J Home | Journal of Mathematics Research | CCSE
%D 2019
%R 10.5539/jmr.v11n2p181
%X 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) ¡ú [0, 1] such that each vertex assigned with 0 has at least two neighbors assigned with 1. The weight of f is ¦²_u¡ÊV(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
%U http://www.ccsenet.org/journal/index.php/jmr/article/view/0/38929