P. Vadapalli and P.K. Srimani, "A new family of Cayley graph interconnection networks of constant degree four," IEEE Transactions on Parallel and Distributed Systems, 7(1)8 January 1996. 16  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... hypercube (a Cayley graph with the same vertex set, degree and connectivity as the hypercube, but a diameter equal to half the diameter of the hypercube) 102] Cayley graphs with n2 n vertices, degree 3 and 4, logarithmic diameter and constructed on signed permutations, 141] 143] [142]. For all these graphs, the authors justify their relevance for interconnection networks by studying their parameters but also algorithms on them (routing, embedding, communication) ffl General theorems are missing which would extend to classes of Cayley graphs properties that have been proved ....

P. Vadapelli and P. Srimani. A new family of Cayley graph interconnection networks of constant degree four. IEEE Trans. Parallel Distrib. Systems, 7(1):26--32, 1996.

....construction, we may only be able to support a fixed number of I O ports at each node, hence we are interested in fixed degree networks. Some fixed degree Cayley graphs are known, e.g. n cycles in [1] the connected cycles in [5] the Cube Connected Cycles in [6] the Cayley graphs proposed in [7], and the k ary n cube which has been used in the design of a number of machines [8, 9, 10, 11, 12] The k ary n cube graphs have even fixed degrees and the other graphs mentioned above have fixed degrees at most 4. In this paper, we propose a new family of Cayley graphs with fixed degree of any ....

....6 and fixed degree of 6, the number of vertices for G 3 4 is 324, while the number of vertices for 5 ary 3 cube, with diameter of 6 and fixed degree of 6, is only 125. With diameter 9 and fixed degree of 6, the number of vertices for G 3 6 is 4374, while that of G 2 6 , the graph proposed in [7], with the same diameter and fixed degree of 4, is 384, and the number of vertices for 7 ary 3 cube, with diameter of 9 and fixed degree of 6, is only 343. Some properties of G k n are shown in Figure 1. The comparison of G k n with some other fixed degree networks such as enhanced hypercubes ....

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P. Vadapalli and K. Srimani, "A new family of Cayley graph interconnection networks of constant degree four," IEEE Transactions on Parallel and Distributed Systems, vol. 7:1, pp. 26--32, Jan 1996.

....network. Guha and Sen [4] gave an optimal algorithm for the undirected de Bruijn graph [10, 11] Liu and Lee [7] gave an optimal routing algorithm for the generalized de Bruijn digraph [3] Meliksetian and Chen [9] gave an optimal routing algorithm for the CCC. Vadapalli and Srimani [13] gave an optimal routing algorithm for the butterfly network (although they did not realize that their proposed new network is in fact the butterfly network [2] Tan et al. 12] proposed the S E E U network (a single stage shuffle exchange and exchange unshuffle network) and its optimal routing ....

P. Vadapalli and P.K. Srimani, "A new family of Cayley graph interconnection networks of constant degree four," IEEE Transactions on Parallel and Distributed Systems, 7(1):26--32, January 1996.

....s Ye s Binary Tree T #m n , 1# T #m n 1# T #m n , 1# T #m n , 1# Mesh of Trees Ye s Ye s Ye s Ye s Figure 1: Hyper deBruijn HD#m;n# and Hyper Butterfly HB#m;n# Graphs Compared z i ; 8i; except for i = 0 #. Recently, the same butterfly topology (with wrap around) Bn is redefined in [4] as a graph on n # 2 n vertices for any integer n, n # 3; each vertex is represented by a cyclic permutation of n symbols in lexicographic order where each symbol may be present in either uncomplemented or complemented form. Let t k , 1 # k # n denote the k th symbol in the set of n symbols. ....

....symmetric (undirected) regular graph of degree 4, has n # 2 n nodes and n # 2 n 1 edges. Bn has a logarithmic diameter D#Bn#=b 3n 2 c and Bn has a vertex connectivity 4, i.e. for any pair of nodes there exist 4 node disjoint paths between them. Bn has many other interesting properties; see [4] for details. Remark 2 It is easy to see the equivalence (isomorphism) between the two interpretations of the wrapped butterfly network graph. We highlight the key features below. Each node in Bn has one of the n possible cyclic permutations of the n symbols (disregarding the complementation of ....

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P. Vadapalli and P. K. Srimani. A new family of Cayley graph interconnection networks of constant degree four. IEEE Transactions on Parallel and Distributed Systems, 7(1), January 1996.

....Cycles [PV81] Most of these graphs, except Cube Connected Cycles, are not regular and they offer low vertex connectivity (fault tolerance) for example, almost all nodes in a De Bruijn graph have a node degree of 4 while the vertex connectivity of the network is only 2. Recently authors in [VS96] have developed a new family of Cayley graphs of constant degree 4 where they have shown that the graph is regular, has a logarithmic diameter and has a vertex connectivity 4 (thus, maximally fault tolerant) an optimal routing algorithm has also been developed. It is to be noted that these graphs ....

....vertex connectivity 4 (thus, maximally fault tolerant) an optimal routing algorithm has also been developed. It is to be noted that these graphs seem to be similar to butterfly network with wraparound [ABR90] Note that Cube Connected Cycles are also regular Cayley graphs, but the graphs TCN n in [VS96] have a higher vertex connectivity (hence higher fault tolerance) and it accommodates a larger number of nodes than cube connected cycle graph for the same diameter. Our purpose in the present paper is to further investigate the topological properties of these tetravalent Cayley networks (we call ....

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P. Vadapalli and P. K. Srimani. A new family of Cayley graph interconnection networks of constant degree four. IEEE Transactions on Parallel and Distributed Systems, 7(1), January 1996.

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P. Vadapalli and P.K. Srimani, "A new family of Cayley graph interconnection networks of constant degree four," IEEE Transactions on Parallel and Distributed Systems, 7(1)8 January 1996. 16

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Premkumar Vadapalli and Pradip K. Srimani. A new family of cayley graph interconnection networks of constant degree four. IEEE Trans. Parallel and Distributed Systems, 7(1):26--32, January 1996.

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