A c-circulant digraph G,(c, A) has Z,V as its vertex set and adjacency rules given by .X + cs + a with a E A c Z,. The c-circulant digraphs of degree two which are isomorphic to some circulant digraph are characterized, and the corresponding isomorphism is given. Moreover. a sufficient condition is obtained for a c-circulant digraph to be a Cayley digraph.

a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...

A digraph D is a 3-anti-circulant digraph, if for any four distinct vertices x1, x2, x3, x4 ∈ V (D), x1 → x2 ← x3 → x4 implies x4 → x1. In this paper, we characterize the structure of 3-anti-circulant digraphs containing a cycle factor and show that the structure is very close to semicomplete and semicomplete bipartite digraphs. Laborde et al. conjectured that every digraph has an independent s...

The Circulant Travelling Salesman Problem (CTSP) is the problem of nding a minimum weight Hamiltonian cycle in a weighted graph with circulant distance matrix. The computational complexity of this problem is not known. In fact, even the complexity of deciding Hamiltonicity of the underlying graph is unkown. This paper presents necessary and suucient conditions for the existence of a Hamilto-nia...

Let F = (Kn,P) be a circulant homogeneous factorisation of index k, that means P is a partition of the arc set of the complete digraph Kn into k circulant factor digraphs such that there exists σ ∈ Sn permuting the factor circulants transitively amongst themselves. Suppose further such an element σ normalises the cyclic regular automorphism group of these circulant factor digraphs, we say F is ...

A circulant is a Cayley digraph over a finite cyclic group. The classification of arc-transitive circulants is shown. The result follows from earlier descriptions of Schur rings over cyclic groups.

For a fixed positive integer n, let Wn be the permutation matrix corresponding to the permutation ( 1 2 · · · n− 1 n 2 3 · · · n 1 ) . In this article, it is shown that a symmetric matrix with rational entries is circulant if, and only if, it lies in the subalgebra of Q[x]/〈x−1〉 generated by Wn+W −1 n . On the basis of this, the singularity of graphs on n-vertices is characterized algebraically...

The dichromatic number dc(D) of a digraph D is the smallest number of colours needed to colour the vertices of D so that no monochromatic directed cycle is created. In this paper the problem of computing the dichromatic number of a Zykov-sum of digraphs over a digraph D is reduced to that of computing a multicovering number of an hypergraph H1(D) associated to D in a natural way. This result al...

We prove that, for a positive integer n and subgroup H of automorphisms of a cyclic group Z of order n, there is up to isomorphism a unique connected circulant digraph based on Z admitting an arc-transitive action of ZzH. We refine the Kovács–Li classification of arc-transitive circulants to determine those digraphs with automorphism group larger than ZzH. As an application we construct, for ea...