Structural Properties and Conditional Diagnosability of Star Graphs by Using the PMC Model

Abstract

Processor fault diagnosis has played an important role in measuring the reliability of a multiprocessor system; the diagnosability of many well-known multiprocessor systems has been widely investigated. Conditional diagnosability is a novel measure of diagnosability. It includes a condition whereby any fault set cannot contain all the neighbors of any node in a system. In this paper, the conditional diagnosability of star graphs by using the PMC model is evaluated. Several new structural properties of star graphs are derived. Based on these properties, the conditional diagnosability of an n-dimensional star graph is determined to be 8n À 21 for n ! 5.

The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks

“…Sengupta and Dahbura [8] proposed a special case of the MM model, called the MM* model, in which each node must test its any pair of adjacent nodes. Numerous studies have been investigated under the PMC model and MM model or MM* model, see [7,10,16,23,27,40].…”

“…For details, see [7,9,[12][13][14]18,19,21,22,[29][30][31][32]39]. The diagnosabilities of the star graph under the PMC model and MM model were studied in [17,43].…”

Conditional diagnosability of bubble-sort star graphs

“…We consider the following cases. 3, 5}), then u 6 (or u 2 ) is a neighbor of u with u 6 ̸ ∈ F 1 (or u 2 ̸ ∈ F 2 ). If u = u i (i ∈ {2, 4, 6}), then u 3 (or u 1 ) is a neighbor of u with u 3 ̸ ∈ F 1 (or u 1 ̸ ∈ F 2 ).…”

Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees under the PMC Model

“…Based on this assumption, Lai et al [2005] introduced the concept of conditional diagnosability and showed that the conditional diagnosability of an ndimensional hypercube Q n is 4n − 7 for n ≥ 5 under the PMC model. Several studies also contributed to the conditional diagnosability of multiprocessor systems under both the PMC and MM* models, including hypercubes [Hsu et al 2009;Lai et al 2005], star graphs [Chang and Hsieh 2014;Cheng et al 2012;Lin et al 2008], k-ary n-cubes Hsieh and Kao 2013], Bijective Connection (BC) networks Xu et al 2009;Zhu 2008], Cayley graphs (only in the MM* model) [Lin et al 2008], and folded hypercubes (PMC) . In this article, we evaluate the conditional diagnosability for n under the PMC model and show it is 4n − 11 for n ≥ 4.…”

“…Several known structural properties of Cayley graphs are exhibited. Based on these properties, we investigate the conditional diagnosability of Cayley graphs generated by transposition trees under the PMC model and show that it is 4n − 11 for n ≥ 4 except for the n-dimensional star graph for which it has been shown to be 8n−21 for n ≥ 5 (refer to Chang and Hsieh [2014]). …”