Non-inclusive g-good-neighbour diagnosability of hypercubes

Abstract

To better measure the fault tolerance and reliability of a network, Yuan et al. introduced the non-inclusive g-good-neighbour diagnosability of a network. The g-good-neighbour faulty set is a special faulty set, which satisfies that every fault-free vertex has at least g fault-free neighbours. The non-inclusive g-good-neighbour diagnosability requires every pair of g-good-neighbour faulty sets is non-inclusive, denoted as t Ng ( G ) . In this paper, we study the non-inclusive g-good-neighbour diagnosability of hypercubes and obtain t Ng ( Q n ) = ( n − 1 − g ) 2 g + 1 + 2 g − 1 for g ∈ { 1 , 2 } under the PMC model, t N 1 ( Q n ) = 3 n − 5 , t N 2 ( Q n ) = 8 n − 21 under the MM* model.