Abstract: In this paper, we consider the skew circulant and skew left circulant matrices with the Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices are also discussed. We obtain the determ...

In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.

The eigenvectors and eigenvalues of block circulant matrices had been found for real symmetric matrices with symmetric submatrices, and for block circulant matrices with circulant submatrices. The eigenvectors are now found for general block circulant matrices, including the Jordan Canonical Form for defective eigenvectors. That analysis is applied to Stephen J. Watson’s alternating circulant m...

Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...

a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graphG of order n is a Cayley graph over the cyclic groupZn: Equivalently, G is circulant i its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent con guration A and, in particular, a S...

Knn odel graphs of even order n and degree 1 blog 2 (n)c, W;n, are graphs which have been introduced some 25 years ago as the topology underlying a time optimal algorithm for gossiping among n nodes Knn o75]. However, they have been formally deened only 5 years ago FP94]. Since then, they have been widely studied as interconnection networks, mainly because of their good properties in terms of b...

A classification of extremal double circulant self-dual codes of lengths up to 88 is known. We demonstrate that there is no extremal double circulant self-dual code of length 90. We give a classification of double circulant self-dual [90, 45, 14] codes. In addition, we demonstrate that every double circulant self-dual [90, 45, 14] code has no extremal selfdual neighbor of length 90. Finally, we...

1 Abstract In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graph G of order n is a Cayley graph over the cyclic group Z n : Equivalently, G is circulant ii its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent connguration A and, in...

‎in this paper‎, ‎we prove the nonexistence of two weighing matrices of‎ ‎weight 81‎, ‎namely $cw(88,81)$ and $cw(99,81)$‎. ‎we will apply two‎ ‎very different methods to do so; for the case of $cw(88,81)$‎, ‎we‎  ‎will use almost purely counting methods‎, ‎while for $cw(99,81)$‎, ‎we‎ ‎will use algebraic methods‎.