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2009年04月19日

【期刊论文】A Simple Method for Computing Resistance Distance

肖文俊, Ravindra B. Bapat, Ivan Gutman a, b, and Wenjun Xiao b

Z. Naturforsch. 58a, 494-498 (2003); received August 2, 2003,-0001,():

-1年11月30日

摘要

The resistance distance ri j between two vertices vi and vj of a (connected, molecular) graph G is equal to the effective resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any edge is unity. We show how ri j can be computed from the Laplacian matrix L of the graph G: Let L(i) and L(i, j) be obtained from L by deleting its i-th row and column, and by deleting its i-th and j-th rows and columns, respectively. Then ri j=detL(i, j)/detL(i).

Resistance Distance, Laplacian Matrix, Kirchhoff Index, Molecular Graph.,

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2009年04月19日

【期刊论文】Cayley graphs as models of deterministic small-world networks

肖文俊, Wenjun Xiao a, Behrooz Parhami b, ∗

Information Processing Letters 97(2006)115-117,-0001,():

-1年11月30日

摘要

Many real networks, including those in social, technological, and biological realms, are small-world networks. The two distinguishing characteristics of small-world networks are high local clustering and small average internode distance. A great deal of previous research on small-world networks has been based on probabilistic methods, with a rather small number of researchers advocating deterministic models. In this paper, we further the study of deterministic small-world networks and show that Cayley graphs may be good models for such networks. Small-world networks based on Cayley graphs possess simple structures and significant adaptability. The Cayley-graph model has pedagogical value and can also be used for designing and analyzing communication and the other real networks.

Average internode distance, Cayley graph, Clustering coefficient, Interconnection network, Low-diameter network

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2009年04月19日

【期刊论文】Some mathematical properties of Cayley digraphs with applications to interconnection network design

肖文俊, WENJUN XIAO†‡ and BEHROOZ PARHAMI*§

International Journal of Computer Mathematics Vol. 82, No. 5, May 2005, 521-528,-0001,():

-1年11月30日

摘要

We consider the relationships between Cayley digraphs and their coset graphs with respect to subgroups and obtain some general results on homomorphism and broadcasting between them. We also derive a general factorization theorem on subgraphs of Cayley digraphs by their automorphism groups. We discuss the applications of these results to well-known interconnection networks such as the butterfly network, the de Bruijn network, the cube-connected cycles network and the shuffle-exchange network.

Broadcasting, Cayley digraphs, Coset graphs, Cross-product graphs, Digraphs, Graph factorization, Homomorphism, Interconnection networks, Parallel processing

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2009年04月19日

【期刊论文】DIAMETER FORMULAS FOR A CLASS OF UNDIRECTED DOUBLE-LOOP NETWORKS

肖文俊, BAOXING CHEN, WENJUN XIAO, BEHROOZ PARHAMI

,-0001,():

-1年11月30日

摘要

An n-node network, with nodes numbered 0 to n-1, is an undirected double-loop network with chord lengths 1 and s (2≤s<hi2) when each node i (0≤i<n) is connected to each of the four nodes i±1 and i±s via an undirected link; all node-index expressions are evaluated modulo n. Let n=qs+r, where r (0≤r<s) is the remainder of dividing n by s. Furthermore, let s=ar+b, where b (0≤b<r) is the remainder of dividing s by r. In this paper, we provide closed-form formulas for the diameter of a double-loop network for the case q>r and for a subcase of the case q≤r when b≤aq+1. In the complementary subcase of q≤r, when b>aq+1, network diameter can be derived by applying the O(log n)-time algorithm of Zerovnik and Pisanski (J.Algorithms, Vol. 14, pp. 226-243, 1993). Obtaining a closed-form formula for diameter of the double-loop network in the latter subcase remains an open problem.

Chordal ring, Loop network, Network diameter, Parallel processing, Ring network, Routing distance, Undirected graph

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2009年04月19日

【期刊论文】Resistance Distance and Laplacian Spectrum

肖文俊, Wenjun Xiao, Ivan Gutman

,-0001,():

-1年11月30日

摘要

The resistance distance rij between two vertices vi and t,,j of a (connected, molecular) graph G is equal to the resistance between the respective two points of all electrical network, constructed so as to correspond to G, such that the resistance of ally two adjacent points is unity. We show how the matrix elements rij call be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||rij||.

Resistance distance-Kirchhoffindex-Laplacian spectrmn

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    华南理工大学,广东

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