Given a digraph D = (V, A), a quasi-kernel of D is an independent set Q C_ V such that for every vertex v not contained in Q, either there exists a vertex u E Q such that v dominates u, or there exists a vertex w such that v dominates w and w dominates some vertex u E Q. A sink in a digraph D = (V, A) is a vertex v E V that dominates no vertex of D. In this thesis we prove that if D is a semico...

A digraph D is called a kernel-perfect digraph or KP -digraph when every induced subdigraph of D has a kernel. We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows: V (ζ(D)) = V (D), and A (ζ(D)) ...

Various results on factorisations of complete graphs into circulant graphs and on 2factorisations of these circulant graphs are proved. As a consequence, a number of new results on the Oberwolfach Problem are obtained. For example, a complete solution to the Oberwolfach Problem is given for every 2-regular graph of order 2p where p ≡ 5 (mod 8) is prime.

A classification of all extremal double circulant self-dual codes of lengths up to 72 is known. In this paper, we give a classification of all extremal double circulant self-dual codes of lengths 74–88. © 2006 Elsevier B.V. All rights reserved.

A multilevel circulant is defined as a graph whose adjacency matrix has a certain block decomposition into circulant matrices. A general algebraic method for finding the eigenvectors and the eigenvalues of multilevel circulants is given. Several classes of graphs, including regular polyhedra, suns, and cylinders can be analyzed using this scheme.

A set of fast real transforms including the well known Hartley transform is fully investigated. Mixed radix splitting properties of Hartley-type transforms are examined in detail. The matrix algebras diagonalized by the Hartley-type matrices are expressed in terms of circulant and (−1)-circulant matrices. © 2002 Elsevier Science Inc. All rights reserved.

Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a SAC 2004 paper, Junod et. al. constructed a new class of efficient MDS matrices whose submatrices were circulant matrices and th...

Consider the powers of a square matrix A of order n in bottleneck algebra, where addition and multiplication are replaced by the max and min operations. The powers are periodic, starting from a certain power AK . The smallest such K is called the exponent of A and the length of the period is called the index of A. Cechlárová has characterized the matrices of index 1. Here we consider the case w...

In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure double circulant i.e. could not be represented in systematic form. Keywords—convolutional encoding, quasi-cyclic codes weight enumeratorg, double circulant