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

Abstract

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.

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

“…For details, see [3]. Recently, Wang et al [6] studied the 2-good-neighbor connectivity and 2good-neighbor diagnosability of bubble-sort star graph networks. Yu and Huang [4] proved that the 2-extra vertex connectivity of the modified bubble-sort graph was 3n − 5.…”

“…So, 5 ≤ |F| ≤ 11. We decompose B 6 along the last position, denoted by [2,6] | � 0. B [2,6] 6 is connected by Claim 1.…”

Edge-Bipancyclicity of Bubble-Sort Star Graphs

“…Gu et al [8] determined the pessimistic diagnosability of BS n . Wang et al [21,22] studied the 2-extra connectivity (resp. 2-good-neighbor connectivity) and the 2-extra diagnosability (resp.…”

g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model and MM* Model

“…In [7], Wang and Han studied the g-good-neighbor diagnosability of the n-dimensional hypercube under the MM* model. There is a significant amount of research on the g-good-neighbor diagnosability of graphs [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”