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...

There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. In this paper we give new families of dense vertex-symmetric...

A digraph is odd-cycle-symmetric if every arc in any elementary odd directed cycle has the reverse arc. This concept arises in the context of the even factor problems, which generalize the path-matching problems. While the even factor problem is NP-hard in general digraphs, it is solvable in polynomial time for odd-cycle-symmetric digraphs. This paper provides a characterization of odd-cycle-sy...

A primitive digraph D is said to be well primitive if the local exponents of D are all equal. In this paper we consider well primitive digraphs of two special types: digraphs that contain loops, and symmetric digraphs with shortest odd cycle of length r. We show that the upper bound of the exponent of the well primitive digraph is n− 1 in both these classes of digraphs, and we characterize the ...

The concept of (k, l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [?] proved a sufficient condition for a digraph to have a (k, l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k, l)-...

It is known that signed graphs with all cycles negative are those in which each block is a negative cycle or a single line. We now study the more difficult problem for signed digraphs. In particular we investigate the structure of those digraphs whose arcs can be signed (positive or negative) so that every (directed) cycle is negative. Such digraphs are important because they are associated wit...