Journal ArticleDOI
A comparative study of topological properties of hypercubes and star graphs
Khaled Day,Anand Tripathi +1 more
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The authors determine necessary and sufficient conditions for shortest path routing and characterize maximum-sized families of parallel paths between any two nodes of the star graph, and parallel paths are proven of minimum length within a small additive constant.Abstract:
Undertakes a comparative study of two important interconnection network topologies: the star graph and the hypercube, from the graph theory point of view. Topological properties are derived for the star graph and are compared with the corresponding properties of the hypercube. Among other results, the authors determine necessary and sufficient conditions for shortest path routing and characterize maximum-sized families of parallel paths between any two nodes of the star graph. These parallel paths are proven of minimum length within a small additive constant. They also define greedy and asymptotically balanced spanning trees to support broadcasting and personalized communication on the star graph. These results confirm the already claimed topological superiority of the star graph over the hypercube. >read more
Citations
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Book ChapterDOI
Cayley graphs and interconnection networks
TL;DR: This work first surveys some classes of Cayley graphs which are well studied as models of interconnection networks, with emphasis on loads of nodes and links in routings.
Journal ArticleDOI
Arrangement graphs: a class of generalized star graphs
Khaled Day,Anand Tripathi +1 more
TL;DR: A new interconnection topology is presented, called the arrangement graph, as a generalization of the star graph topology and many of its properties such as: hierarchical structure, vertex and edge symmetry, simple and optimal routing, and many fault tolerance properties are proved.
Journal ArticleDOI
Cayley graphs as classifiers for data mining: The influence of asymmetries
TL;DR: This paper proposes a new method of using Cayley graphs for classification of data using the endomorphism monoids of graphs, a convenient tools expressing asymmetries of the graphs.
Journal ArticleDOI
Fault-tolerant ring embedding in a star graph with both link and node failures
TL;DR: This paper considers an injured star graph with some faulty links and nodes, and shows that even with f/sub e//spl les/n-3 faulty links, a Hamiltonian cycle still can be found in an n-star, and that an embedding is able to establish a ring containing at least n!-4f/sub v/ nodes.
Journal ArticleDOI
On the fault-diameter of the star graph
TL;DR: The fault-diameter of the star graph is derived using a combinatorial method based on counting the number of node-disjoint paths of optimal length between a given pair of nodes in the graph and distributing the faulty nodes among these paths in a worst-case fashion.
References
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Journal ArticleDOI
Topological properties of hypercubes
Y. Saad,M.H. Schultz +1 more
TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.
Proceedings Article
A Group Theoretic Model for Symmetric Interconnection Networks.
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