We show in this paper that the circulant graph G( 2”‘, 4) is Hamiltonian decomposable, and propose a recursive construction method. This is a partial answer to a problem posed by B. Alspach. @ 1997 Published by Elsevier Science B.V.

The generalized recursive circulant networking can be widely used in the design and implementation of interconnection networks. It consists a series processors, each is connected through bidirectional, point-to-point communication channels to different neighbors. In this work, we apply shortest path routing concept build independent spanning trees on graphs. proposed strategy loosen restricted ...

Two spanning trees of a graph G are said to be independent if they are rooted at the same vertex r, and for each vertex v 6= r in G, the two different paths from v to r, one path in each tree, are internally disjoint. A set of spanning trees of G is independent if they are pairwise independent. A recursive circulant graph G(N, d) has N = cdm vertices labeled from 0 to N − 1, where d > 2, m > 1,...

For the interconnection network topology, it is usually represented by a graph. When a network is used, processors and/or links faults may happen. Thus, it is meaningful to consider faulty networks. We consider k-regular graphs in this paper. We define a k-regular hamiltonian and hamiltonian connected graph G is super fault-tolerant hamiltonian if G remains hamiltonian after removing at most k ...

A paired many-to-many -disjoint path cover (paired -DPC) of a graph  is a set of  disjoint paths joining  distinct source-sink pairs in which each vertex of  is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants   with ≥  and tori, and show that provided the number of faulty elements (vertices and/or edges) is  or less, every nonbiparti...

Calculating the permanent of a (0, 1) matrix is a #P -complete problem but there are some classes of structuredmatrices for which the permanent is calculable in polynomial time. The most well-known example is the fixedjump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constant-coefficient fixed-order recurrence relation. In this note we show how, by i...

The graph G(N; d) has vertex set V = {0; 1; : : : ; N − 1}, with {v; w} an edge if v − w ≡ ±di(modN ) for some 06i6dlogd Ne − 1. We show that the circulant graph G(cd; d) is Hamilton decomposable for all positive integers c; d, and m with c¡d. This extends work of Micheneau and answers a special case of a question of Alspach. c © 2000 Elsevier Science B.V. All rights reserved.

The recursive algorithm of a (fast) discrete wavelet transform, as well as its generalizations, can be described as repeated applications of block-Toeplitz operators or, in the case of periodized wavelets, multiplications by block circulant matrices. Singular values of a block circulant matrix are the singular values of some matrix trigonometric series evaluated at certain points. The norm of a...

Calculating the permanent of a (0, 1) matrix is a #P -complete problem but there are some classes of structuredmatrices for which the permanent is calculable in polynomial time. The most well-known example is the fixed-jump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constant-coefficient fixed-order recurrence relation. In this note we show how, by ...

Calculating the permanent of a (0, 1) matrix is a #P complete problem but there are some classes of structured matrices for which the permanent is calculable in polynomial time. The most well-known example is the fixed-jump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constantcoefficient fixed-order recurrence relation. In this note we show how, by i...