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Fault Tolerance and 2-Domination in Certain Interconnection Networks

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  • Lian Chen
  • Xiujun Zhang

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.

Suggested Citation

  • Lian Chen & Xiujun Zhang, 2019. "Fault Tolerance and 2-Domination in Certain Interconnection Networks," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 181-189, April.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:2:p:181
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    References listed on IDEAS

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    1. S. Robin & J.-J. Daudin, 2001. "Exact Distribution of the Distances between Any Occurrences of a Set of Words," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 895-905, December.
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    More about this item

    Keywords

    fault tolerance; 2-domination; mesh; cylinder; torus;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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