Introduction By Ghouila-Houri's theorem [10], every strong digraph of order n and with minimum degree at least n is Hamiltonian. Extensions of this theorem can be found in [11, 13, 16, 18]. Nash-Williams [15] raised the problem of describing all the extreme digraphs for Ghouila-Houri's theorem, i.e. the strong non-Hamiltonian digraphs of order n and minimum degree n — 1. Bondy [4] specialized t...

In this paper we study the complementarity spectrum of digraphs, with special attention to problem digraph characterization through spectrum. That is, whether two non-isomorphic digraphs same number vertices can have eigenvalues. The eigenvalues matrices, also called Pareto eigenvalues, has led (undirected) graphs and, in particular, undirected these is an open problem. We characterize one and ...

Cycle pre x digraphs are a class of Cayley coset graphs with many remarkable properties such as symmetry large number of nodes for a given degree and diameter simple shortest path routing Hamiltonic ity optimal connectivity and others In this paper we show that the cycle pre x digraphs like the Kautz digraphs contain cycles of all lengths l with l between two and N the order of the digraph exce...

A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with Ug = V . Here, extending work of Lachlan on finite homogeneous digraphs, we classify finite set-homogeneous digraphs, where we allow some pairs of vertices to have arcs in both directions. Under the assumption that such pairs of vertices are not allowed, we ...

In this paper we investigate new sufficient conditions for a digraph to be kernel-perfect (KP) and some structural properties of kernel-perfect critical (KPC) digraphs. In particular, it is proved that the asymmetrical part of any KPC digraph is strongly connected. A new method to construct KPC digraphs is developed. The existence of KP and KPC digraphs with arbitrarily large dichromatic number...

Since Moore digraphs do not exist for k 6= 1 and d 6= 1, the problem of finding digraphs of out-degree d ≥ 2, diameter k ≥ 2 and order close to the Moore bound, becomes an interesting problem. To prove the non-existence of such digraphs or to assist in their construction (if they exist), we first may wish to establish some properties that such digraphs must possess. In this paper we consider th...

We consider the problem (MSSS) of nding a strongly connected spanning subgraph with the minimum number of arcs in a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamil-tonian cycle problem. We show that the problem is polynomially solvable for quasi-transitive digraphs. We describe the minimum number of arcs in such a spanning subgraph of a qu...

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v, w ∈ V (D), (u, v), (v, w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈...