scholarly journals Conditional Strong Matching Preclusion of the Alternating Group Graph

2019 ◽  
Vol 06 (02) ◽  
pp. 1-16
Author(s):  
Mohamad Abdallah ◽  
◽  
Eddie Cheng ◽  
Keyword(s):  
Alternating Group ◽  
Alternating Group Graph

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.

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.

THE Qn,k,m GRAPH: A COMMON GENERALIZATION OF VARIOUS POPULAR INTERCONNECTION NETWORKS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350011 ◽  
Author(s):  
EDDIE CHENG ◽  
NART SHAWASH
Keyword(s):  
Interconnection Networks ◽  
Cayley Graphs ◽  
Alternating Group ◽  
Star Graph ◽  
Strong Connectivity ◽  
Common Generalization ◽  
Arrangement Graph ◽  
Special Case ◽  
Alternating Group Graph

The star graph and the alternating group graph were introduced as competitive alternatives to the hypercube, and they are indeed superior over the hypercube under many measures. However, they do suffer from scaling issues. To address this, different generalizations, namely, the (n,k)-star graph and the arrangement graph were introduced to address this shortcoming. From another direction, the star graph was recognized as a special case of Cayley graphs whose generators can be associated with a tree. Nevertheless, all these networks appear to be very different and yet share many properties. In this paper, we will solve this mystery by providing a common generalization of all these networks. Moreover, we will show that these networks have strong connectivity properties.

Subgraph Reliability of Alternating Group Graph With Uniform and Nonuniform Vertex Fault-Free Probabilities

2020 ◽  
Author(s):  
Yanze Huang ◽  
Limei Lin ◽  
Li Xu
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Fault Model ◽  
Alternating Group ◽  
Multiprocessor System ◽  
Single Vertex ◽  
Arrangement Graph ◽  
Uniform Probability ◽  
Better Than ◽  
Alternating Group Graph

Abstract As the size of a multiprocessor system grows, the probability that faults occur in this system increases. One measure of the reliability of a multiprocessor system is the probability that a fault-free subsystem of a certain size still exists with the presence of individual faults. In this paper, we use the probabilistic fault model to establish the subgraph reliability for $AG_n$, the $n$-dimensional alternating group graph. More precisely, we first analyze the probability $R_n^{n-1}(p)$ that at least one subgraph with dimension $n-1$ is fault-free in $AG_n$, when given a uniform probability of a single vertex being fault-free. Since subgraphs of $AG_n$ intersect in rather complicated manners, we resort to the principle of inclusion–exclusion by considering intersections of up to five subgraphs and obtain an upper bound of the probability. Then we consider the probabilistic fault model when the probability of a single vertex being fault-free is nonuniform, and we show that the upper bound under these two models is very close to the lower bound obtained in a previous result, and it is better than the upper bound deduced from that of the arrangement graph, which means that the upper bound we obtained is very tight.

An Analysis on the Reliability of the Alternating Group Graph

2021 ◽  
pp. 1-14
Author(s):  
Limei Lin ◽  
Yanze Huang ◽  
Yuhang Lin ◽  
Li Xu ◽  
Sun-Yuan Hsieh
Keyword(s):  
Alternating Group ◽  
Alternating Group Graph
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