Fault-tolerant maximal local-connectivity on Bubble-sort star graphs

Discrete Applied Mathematics

2017

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 bubblesort star graph BS n has many good properties. In this paper, we prove that 2-good-neighbor connectivity of BS n is 8n − 22 for n ≥ 5 and the 2-good-neighbor connectivity of BS 4 is 8; the 2-good-neighbor diagnosability of BS n is 8n − 19 under the PMC model and MM * model for n ≥ 5.

Section: The Bubble-sort Star Graphmentioning

confidence: 99%

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

Discrete Applied Mathematics

2017

“…BS n can be embedded in a CW n . CW n surpasses BS n in connectivity [15,16]. Hence, CW n is also a desirable processing model.…”

Section: E Wheel Networkmentioning

confidence: 99%

2-Restricted Edge Connectivity of Wheel Networks

Feng

Mathematical Problems in Engineering

2021

The g -restricted edge connectivity ( g -REC) is an efficient index in evaluating the reliability and fault tolerance of large-scale processing systems. Assume that G = V , E is a simple connected graph and F ⊆ E . The g -REC of G , denoted by λ g G , is the minimum F such that G − F is disconnected and any component has at least g nodes. The n -dimensional wheel network CW n , a kind of Cayley graph, possesses many desired features. In this paper, we establish that λ 2 CW n is 4 n − 6 for n ≥ 5 , and CW n is λ 2 -optimal.

“…It is easy to verify MB i n � B n− 1 . B n is well studied by other researchers [9][10][11][12][13]. B n has some small hypercubes Q k as subgraphs [14].…”

Section: E Modified Bubble-sort Graphmentioning

confidence: 99%

The 3-Good-Neighbor Connectivity of Modified Bubble-Sort Graphs

Mathematical Problems in Engineering

2020

Let G = V G , E G be a connected graph. A subset F ⊆ V G is called a g -good-neighbor cut if G − F is disconnected and each vertex of G − F has at least g neighbors. The g -good-neighbor connectivity of G is the minimum cardinality of g -good-neighbor cuts. The n -dimensional modified bubble-sort graph MB n is a special Cayley graph. It has many good properties. In this paper, we prove that the 3-good-neighbor connectivity of MB n is 8 n − 24 for n ≥ 6 .