In this paper, we study the existence of cycles of all lengths in the recursive circulant graphs, and we show a necessary and sufficient condition for the graph being pancyclic and bipancyclic.  2002 Elsevier Science B.V. All rights reserved.

Let γ(n, δ) denote the largest possible domination number for a graph of order n and minimum degree δ. This paper is concerned with the behavior of the right side of the sequence n = γ(n, 0) ≥ γ(n, 1) ≥ · · · ≥ γ(n, n− 1) = 1. We set δk(n) = max{δ | γ(n, δ) ≥ k}, k ≥ 1. Our main result is that for any fixed k ≥ 2 there is a constant ck such that for sufficiently large n, n− ckn ≤ δk+1(n) ≤ n− n...

With the help of some new results about weight enumerators of self-dual codes overZ4 we investigate a class of double circulant codes over Z4, one of which leads to an extremal even unimodular 40-dimensional lattice. It is conjectured that there should be “Nine more constructions of the Leech lattice”.

We obtain explicit formulae for the values of the 2v − j minors, j = 0, 1, 2, of Doptimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2−{2s2+2s+1; s2, s2; s(s−1)} supplementary difference sets (sds). This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our t...

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian mat...

Sampling and budgeting training examples are two essential factors in tracking algorithms based on support vector machines (SVMs) as a tradeoff between accuracy and efficiency. Recently, the circulant matrix formed by dense sampling of translated image patches has been utilized in correlation filters for fast tracking. In this paper, we derive an equivalent formulation of a SVM model with circu...

We propose geometrical methods for constructing square 01-matrices with the same number n of units in every row and column, and such that any two rows of the matrix contain at most one unit in common. These matrices are equivalent to n-regular bipartite graphs without 4-cycles, and therefore can be used for the construction of efficient bipartite-graph codes such that both the classes of its ve...

We present a new bound for suprema of a special type of chaos processes indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time-frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sp...

We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors. By deriving improved variance bounds related to binary Gaussian circulant embeddings, we largely fix a gap in the proof of the best known fast binary embedding method. Our bounds also show that well-spreadness assumptions...

Boundary value methods (BVMs) for ordinary di erential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditio...