The g-good-neighbor and g-extra diagnosability of networks

Abstract

Diagnosability of a multiprocessor system is an important research topic. The system and interconnection network has a underlying topology, which usually presented by a graph G=(V,E). In 2012, a measurement for fault tolerance of the graph was proposed by Peng et al. This measurement is called the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. In 2016, Zhang et al. proposed a new measurement for fault diagnosis of the graph, namely, the g-extra diagnosability, which restrains that every fault-free component has at least (g+1) fault-free nodes. A fault set F⊆V is called a g-good-neighbor faulty set if the degree d(v)≥g for every vertex v in G−F. A g-good-neighbor cut of G is a g-good-neighbor faulty set F such that G−F is disconnected. The minimum cardinality of g-good-neighbor cuts is said to be the g-good-neighbor connectivity of G. A fault set F⊆V is called a g-extra faulty set if every component of G−F has at least (g+1) vertices. A g-extra cut of G is a g-extra faulty set F such that G−F is disconnected. The minimum cardinality of g-extra cuts is said to be the g-extra connectivity of G. The g-good-neighbor (extra) diagnosability and g-good-neighbor (extra) connectivity of many well-known graphs have been widely investigated. In this paper, we show the relationship between the g-good-neighbor (extra) diagnosability and g-good-neighbor (extra) connectivity of graphs.