Conditional diagnosability of Cayley graphs generated by wheel graphs under the PMC model

2021 ◽  
Vol 849 ◽  
pp. 163-172
Author(s):  
Yulong Wei ◽  
Min Xu
Keyword(s):  
Cayley Graphs ◽  
Pmc Model ◽  
Wheel Graphs ◽  
Conditional Diagnosability

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

2015 ◽  
Vol 20 (2) ◽  
pp. 1-16 ◽  
Author(s):  
Naiwen Chang ◽  
Eddie Cheng ◽  
Sunyuan Hsieh
Keyword(s):  
Cayley Graphs ◽  
Pmc Model ◽  
Conditional Diagnosability

A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs

2019 ◽  
Vol 63 (9) ◽  
pp. 1372-1384
Author(s):  
Zuwen Luo ◽  
Liqiong Xu
Keyword(s):  
Fault Tolerance ◽  
Connected Graph ◽  
Cayley Graphs ◽  
Network Structures ◽  
Vertex Connectivity ◽  
Wheel Graphs

Abstract Let $G=(V(G), E(G))$ be a connected graph. A subset $T \subseteq V(G)$ is called an $R^{k}$-vertex-cut, if $G-T$ is disconnected and each vertex in $V(G)-T$ has at least $k$ neighbors in $G-T$. The cardinality of a minimum $R^{k}$-vertex-cut is the $R^{k}$-vertex-connectivity of $G$ and is denoted by $\kappa ^{k}(G)$. $R^{k}$-vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study $R^{1}$-vertex-connectivity and $R^{2}$-vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by $AW_{n}$, and show that $\kappa ^{1}(AW_{n})=4n-7$ for $n\geq 6$; $\kappa ^{2}(AW_{n})=6n-12$ for $n\geq 6$.

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

Conditional Diagnosability of Matching Composition Networks Under the PMC Model

2009 ◽  
Vol 56 (11) ◽  
pp. 875-879 ◽  
Author(s):  
Min Xu ◽  
K. Thulasiraman ◽  
Xiao-Dong Hu
Keyword(s):  
Pmc Model ◽  
Conditional Diagnosability

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

2016 ◽  
Vol 628 ◽  
pp. 92-100 ◽  
Author(s):  
Mujiangshan Wang ◽  
Yuqing Lin ◽  
Shiying Wang
Keyword(s):  
Cayley Graphs ◽  
Pmc Model ◽  
Good Neighbor

Conditional Diagnosability of Augmented Cubes under the PMC Model

2012 ◽  
Vol 9 (1) ◽  
pp. 46-60 ◽  
Author(s):  
Nai-Wen Chang ◽  
Sun-Yuan Hsieh
Keyword(s):  
Pmc Model ◽  
Conditional Diagnosability

Conditional Diagnosability of Burnt Pancake Networks Under the PMC Model

2015 ◽  
pp. bxv066 ◽  
Author(s):  
Sulin Song ◽  
Shuming Zhou ◽  
Xiaoyan Li
Keyword(s):  
Pmc Model ◽  
Conditional Diagnosability

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 kind of conditional connectivity of Cayley graphs generated by wheel graphs

2017 ◽  
Vol 301 ◽  
pp. 177-186 ◽  
Author(s):  
Jianhua Tu ◽  
Yukang Zhou ◽  
Guifu Su
Keyword(s):  
Cayley Graphs ◽  
Wheel Graphs
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