On the Problem of Determining which (n, k)-Star Graphs are Cayley Graphs (original) (raw)
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A Complete Classification of Which (n, k)-Star Graphs are Cayley Graphs
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The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs and Combinatorics 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.
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arXiv (Cornell University), 2017
The (n, k)-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al. (Graphs and Combinatorics 2017) and complete the classification of all the (n, k)-star graphs that are Cayley.
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1994 International Conference on Parallel Processing-Vol 1 (ICPP'94), 1994
Most of the popular interconnection networks can be represented as Cayley graphs. Star graph is one of the extensively studied undirected 1 Cayley graphs, which is considered to be an attractive alternative to the popular binary n-cube. The n-rotator graph and the cycle pre x digraph are a set of directed Cayley graphs introduced recently. Since the recently introduced directed Cayley graphs have some interesting properties, a comparative study of star and directed Cayley graphs is worthy of study. In this paper we compare the structural and algorithmic aspects of star graphs with that of directed Cayley graphs. In the process we present some new results for star graphs and directed Cayley graphs. We present a formula to calculate the number of nodes at any distance from the identity permutation in star graphs. The minimum bisection width of star and rotator graphs is obtained. Partitioning and fault tolerant parameters for both star and directed Cayley graphs are analyzed. The node disjoint parallel paths and hence the upper bound on the fault diameter of rotator graphs are presented. We compare the minimal path routing in star and rotator graphs using simulation results. Broadcasting and embedding in star and directed Cayley graphs are also compared.
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The decomposition of complex networks into smaller, interconnected components is a central challenge in network theory with a wide range of potential applications. In this paper, we utilize tools from group theory and ring theory to study this problem when the network is a Cayley graph. In particular, we answer the following question: Which Cayley graphs are prime?
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Iraqi Journal of Science
Suppose that is a finite group and is a non-empty subset of such that and . Suppose that is the Cayley graph whose vertices are all elements of and two vertices and are adjacent if and only if . In this paper, we introduce the generalized Cayley graph denoted by that is a graph with vertex set consists of all column matrices which all components are in and two vertices and are adjacent if and only if , where is a column matrix that each entry is the inverse of similar entry of and is matrix with all entries in , is the transpose of and . In this paper, we clarify some basic properties of the new graph and assign the structure of when is complete graph , complete bipartite graph and complete 3-partite graph for every .
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Nowadays data centers are becoming huge facilities with hundreds of thousands of nodes, connected through a network. The design of such interconnection networks involves finding graph models that have good topological properties and that allow the use of efficient routing algorithms. Cayley Graphs, a kind of graphs that represents an algebraic group, meet these properties and therefore have been proposed as a model for these networks. In this paper we present a routing algorithm based on Shortlex Automatic Structure, which can be used on any interconnection network with an underlying Cayley Graph (of some finite group). We show that our proposal computes the shortest path between any two vertices with low time and space complexity in comparison with traditional routing algorithms.