Shiying Wang

The 2-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model

Diagnosability is an important metric for measuring the reliability of multiprocessor systems. In 2012, Peng et al. proposed a new measure for fault diagnosis of the system, which is called g-good-neighbor diagnosability that restrains every fault-free node containing at least g fault-free neighbors. As a favorable topology structure of interconnection networks, the Cayley graph C ? n generated by the transposition tree ? n has many good properties. In this paper, we give that the 2-good-neighbor diagnosability of C ? n under the PMC model and MM* model is g ( n - 2 ) - 1 , where n ? 4 and g is the girth of C ? n .

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

Connectivity plays an important role in measuring the fault tolerance of interconnection networks. The g -good-neighbor connectivity of an interconnection network G is the minimum cardinality of g -good-neighbor cuts. Diagnosability of a multiprocessor system is one important study topic. A new measure for fault diagnosis of the system restrains that every fault-free node has at least g fault-free neighbor vertices, which is called the g -good-neighbor diagnosability of the system. As a famous topology structure of interconnection networks, the n -dimensional bubble-sort star graph B S n has many good properties. In this paper, we prove that 2-good-neighbor connectivity of B S n is 8 n - 22 for n ź 5 and the 2 -good-neighbor connectivity of B S 4 is 8; the 2 -good-neighbor diagnosability of B S n is 8 n - 19 under the PMC model and MM ź model for n ź 5 .

Fault-free Hamiltonian cycles passing through a linear forest in ternary n-cubes with faulty edges

A linear forest in a graph is a subgraph each component of which is a path. In this paper, we investigate the existence of a Hamiltonian cycle passing through a linear forest in a ternary n-cube Qn3 (n?2) with faulty edges. Let F be a faulty edge set of Qn3 and L be a prescribed linear forest in Qn3-F. If |E(L)|?2n-1 and |F|?n-(?|E(L)|/2?+1), then there is a Hamiltonian cycle passing through L in Qn3-F.

k -restricted edge connectivity in ( p + 1 ) -clique-free graphs

Let G be a graph with vertex set V ( G ) and edge set E ( G ) . An edge subset S ? E ( G ) is called a k -restricted edge cut if G - S is not connected and every component of G - S has at least k vertices. The k -restricted edge connectivity of a connected graph G , denoted by λ k ( G ) , is defined as the cardinality of a minimum k -restricted edge cut. Let X , X ? denote the set of edges between a vertex set X ? V ( G ) and its complement X ? = V ( G ) ? X . A vertex set X ? V ( G ) is called a λ k -fragment if X , X ? is a minimum k -restricted edge cut of G . Let ? k ( G ) = min { | X , X ? | : | X | = k , G X is?connected } . In this work, we give a lower bound on the cardinality of λ k -fragments of a graph G satisfying λ k ( G ) < ? k ( G ) and containing no ( p + 1 ) -cliques. As a consequence of this result, we show a sufficient condition for a graph G with λ k ( G ) = ? k ( G ) .

Strong matching preclusion for torus networks

The torus network is one of the most popular interconnection network topologies for massively parallel computing systems. Strong matching preclusion that additionally permits more destructive vertex faults in a graph is a more extensive form of the original matching preclusion that assumes only edge faults. In this paper, we establish the strong matching preclusion number and all minimum strong matching preclusion sets for bipartite torus networks and 2-dimensional nonbipartite torus networks.

The g-good-neighbor diagnosability of locally twisted cubes☆

Abstract Diagnosability of a multiprocessor system is one important measure of the reliability of interconnection networks. In 2012, Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free node containing at least g fault-free neighbors. The locally twisted cube L T Q n is applied widely. In this paper, we give that the g-good-neighbor diagnosability of L T Q n is 2 g ( n − g + 1 ) − 1 under the PMC model and the MM⁎ model for n ≥ 3 and 0 ≤ g ≤ n − 3 .

Embedding various cycles with prescribed paths into k-ary n-cubes

Abstract The k -ary n -cube has been one of the most popular interconnection networks for large-scale multi-processor systems and data centers. In this study, we investigate the problem of embedding cycles of various lengths passing through prescribed paths in the k -ary n -cube. For n ≥ 2 and k ≥ 5 with k odd, we prove that every path with length h ( 1 ≤ h ≤ 2 n − 1 ) in the k -ary n -cube lies on cycles of every length from h + ( k − 1 ) ( n − 1 ) / 2 + k to k n inclusive.

The 1-good-neighbor connectivity and diagnosability of Cayley graphs generated by complete graphs

Abstract Diagnosability is a significant metric to measure the reliability of multiprocessor systems. In 2012, a new measure for fault tolerance of the system was proposed by Peng et al. This measure is called the g -good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. The Cayley graph C K n generated by the complete graph K n has many good properties as other Cayley graphs. In this paper, we show that the connectivity of C K n is n ( n − 1 ) 2 , the 1-good-neighbor connectivity of C K n is n 2 − n − 2 and the 1 -good-neighbor diagnosability of C K n under the PMC model is n 2 − n − 1 for n ≥ 4 and under the MM ∗ model is n 2 − n − 1 for n ≥ 5 .

The connectivity and nature diagnosability of expanded k-ary n-cubes

Connectivity and Diagnosability play an important role in measuring the fault tolerance of interconnection networks. As a topology structure of interconnection networks, the expanded k -ary n -cube X Q k n has many good properties. In this paper, we prove that (1) the connectivity of X Q k n is 4 n ; (2) the nature connectivity of X Q k n is 8 n − 4; (3) the nature diagnosability of X Q k n under the PMC model and MM ∗ model is 8 n − 3 for n ≥ 2.

Embedding fault-free hamiltonian paths with prescribed linear forests into faulty ternary n-cubes

Abstract The k-ary n-cube is an important underlying topology for large-scale multiprocessor systems. A linear forest in a graph is a subgraph each component of which is a path. In this paper, we investigate the problem of embedding hamiltonian paths passing through a prescribed linear forest in ternary n-cubes with faulty edges. Given a faulty edge set F with at most 2 n − 3 edges and a linear forest L with at most 2 n − 3 − | F | edges, for two distinct vertices in the ternary n-cube, we show that the ternary n-cube admits a fault-free hamiltonian path between u and v passing through L if and only if none of the paths in L has u or v as internal vertices or both of them as end-vertices.