scholarly journals The 2-good-neighbor (2-extra) diagnosability of alternating group graph networks under the PMC model and MM* model

2017 ◽  
Vol 305 ◽  
pp. 241-250 ◽  
Author(s):  
Shiying Wang ◽  
Yuxing Yang
Keyword(s):  
Alternating Group ◽  
Pmc Model ◽  
Good Neighbor ◽  
Alternating Group Graph

The 1-Good-Neighbor Conditional Diagnosability of Some Regular Graphs

2017 ◽  
Vol 17 (03n04) ◽  
pp. 1741001
Author(s):  
MEI-MEI GU ◽  
RONG-XIA HAO ◽  
AI-MEI YU
Keyword(s):  
Alternating Group ◽  
Regular Graphs ◽  
Connected Graphs ◽  
Free Vertex ◽  
Pmc Model ◽  
Star Networks ◽  
Conditional Diagnosability ◽  
Good Neighbor

The g-good-neighbor conditional diagnosability is the maximum number of faulty vertices a network can guarantee to identify, under the condition that every fault-free vertex has at least g fault-free neighbors. In this paper, we study the 1-good-neighbor conditional diagnosabilities of some general k-regular k-connected graphs G under the PMC model and the MM* model. The main result [Formula: see text] under some conditions is obtained, where l is the maximum number of common neighbors between any two adjacent vertices in G. Moreover, the following results are derived: [Formula: see text] for the hierarchical star networks, [Formula: see text] for the BC networks, [Formula: see text] for the alternating group graphs [Formula: see text].

A Note on the Nature Diagnosability of Alternating Group Graphs Under the PMC Model and MM* Model

2018 ◽  
Vol 18 (01) ◽  
pp. 1850005 ◽  
Author(s):  
SHIYING WANG ◽  
LINGQI ZHAO
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Alternating Group ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Free Node ◽  
Pmc Model ◽  
Important Study ◽  
Communication Links ◽  
Alternating Group Graph

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4.

g-good-neighbor conditional diagnosability of star graph networks under PMC model and MM* model

2017 ◽  
Vol 12 (5) ◽  
pp. 1221-1234 ◽  
Author(s):  
Shiying Wang ◽  
Zhenhua Wang ◽  
Mujiangshan Wang ◽  
Weiping Han
Keyword(s):  
Star Graph ◽  
Pmc Model ◽  
Conditional Diagnosability ◽  
Star Graph Networks ◽  
Good Neighbor

scholarly journals The g-Good-Neighbor Diagnosability of Bubble-Sort Graphs under Preparata, Metze, and Chien’s (PMC) Model and Maeng and Malek’s (MM)* Model

Information ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 21
Author(s):  
Shiying Wang ◽  
Zhenhua Wang
Keyword(s):  
Fault Diagnosis ◽  
Interconnection Networks ◽  
Multiprocessor System ◽  
Topology Structure ◽  
Free Node ◽  
Pmc Model ◽  
Good Neighbor

Diagnosability of a multiprocessor system is an important topic of study. A 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 graph B n has many good properties. In this paper, we prove that (1) the 1-good-neighbor diagnosability of B n is 2 n − 3 under Preparata, Metze, and Chien’s (PMC) model for n ≥ 4 and Maeng and Malek’s (MM) ∗ model for n ≥ 5 ; (2) the 2-good-neighbor diagnosability of B n is 4 n − 9 under the PMC model and the MM ∗ model for n ≥ 4 ; (3) the 3-good-neighbor diagnosability of B n is 8 n − 25 under the PMC model and the MM ∗ model for n ≥ 7 .

Neighbor Connectivity of the Alternating Group Graph

2021 ◽  
pp. 2150014
Author(s):  
Mohamad Abdallah ◽  
Chun-Nan Hung
Keyword(s):  
Alternating Group ◽  
Empty Graph ◽  
Neighbor Connectivity ◽  
Alternating Group Graph

Given a graph [Formula: see text], its neighbor connectivity is the least number of vertices whose deletion along with their neighbors results in a disconnected, complete, or empty graph. The edge neighbor connectivity is the least number of edges whose deletion along with their endpoints results in a disconnected, complete, or empty graph. In this paper, we determine the neighbor connectivity [Formula: see text] and the edge neighbor connectivity [Formula: see text] of the alternating group graph. We show that [Formula: see text], where [Formula: see text] is the [Formula: see text]-dimensional alternating group graph.

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