Given a finite Abelian group G and a generator subset A ⊂ G of cardinality two, we consider the Cayley digraph Γ = Cay(G, A). This digraph is called 2–Cayley digraph. An extension of Γ is a 2–Cayley digraph, Γ′ = Cay(G′, A) with G < G′, such that there is some subgroup H < G′ satisfying the digraph isomorphism Cay(G′/H, A) ∼= Cay(G, A). We also call the digraph Γ a quotient of Γ′. Notice that t...

We study the convergence to stationarity for random walks on dynamic digraphs with given degree sequences. The undergo full regeneration at independent geometrically distributed time intervals parameter α. Relaxation is result of an interplay and mixing static digraph. When number vertices n tends infinity α zero, we find three scenarios according whether αlogn converges or some finite positive...

A 1-factorisation of a graph G is a partition of the edge set of G into 1factors (perfect matchings); a perfect 1-factorisation of G is a 1-factorisation of G in which the union of any two of the 1-factors is a Hamilton cycle in G. It is known that for bipartite 4-regular circulant graphs, having order 2 (mod 4) is a necessary (but not sufficient) condition for the existence of a perfect 1-fact...

A k x k matrix A = [aU lover a field F is called circulant if aij = a (j-i) mod k' A [2k ,k l linear code over F = GF (q) is called double-circulant if it is generated by a matrix of the fonn [I A l, where A is a circulant matrix. In this work we ftrst employ the Fourier transform techJ nique to analyze and construct se:veral families of double-circulant codes. The minimum distance of the resul...

We disprove the following conjecture due to Vı́ctor Neumann-Lara: for every pair (r, s) of integers such that r > s > 2, there is an infinite set of circulant tournaments T such that the dichromatic number and the cyclic triangle free disconnection of T are equal to r and s, respectively. Let Fr,s denote the set of circulant tournaments T with dc(T ) = r and − →ω 3 (T ) = s. We show that for eve...

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...

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors. Kwak and Lee (Canad. J. Math. XLII (1990) 747) enumerated the isomorphism classes of graph bundles and those of n-fold coverings with respect to a group of automorphisms of the base graph G which 9x a spanning tree. Hofmeister (Discrete Math. 98 (1991) 175) independently enumerated the isomorphism ...