The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined.

Let G be a strongly connected digraph with distance matrix D(G) and let Tr(G) the diagonal vertex transmissions of G. For any real ? [0, 1], define D?(G) as = ?Tr(G) + (1-?)D(G). The D? spectral radius is D?(G). In this paper, we first give some upper lower bounds for characterize extremal digraphs. Moreover, digraphs that are not transmission regular, bound on difference between maximum radius...

We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two (linear) distributed algorithms, deterministic and gossip, respectively for the cases where the inter-agent communication is synchronous and asynchronous. Our contribution is that in both cases, the developed algorithms guarantee state averaging on ar...

We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non necessarily connected.

In this paper we initiate a systematic study of the Reduced Degree Spanning Tree problem, where given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree with at most k vertices of reduced out-degree. This problem is a directed analog of the wellstudied Minimum-Vertex Feedback Edge Set problem. We show that this problem is fixed-parameter tractable and admits a...

Given a digraph D, the complementarity spectrum of is defined as set eigenvalues its adjacency matrix. This has been shown to be useful in several fields, particularly spectral graph theory. The differences between properties for (undirected) graphs and digraphs, makes study latter particular interest, characterizing strongly connected digraphs with small number non trivial problem. Recently, o...

A dicut in a directed graph is cut for which all of its edges are to common side the cut. famous theorem Lucchesi and Younger states that every finite digraph least size an edge set meeting equals maximum number disjoint dicuts digraph. In this first paper out series two papers, we conjecture version using more structural description min-max property infinite digraphs. We show can be reduced co...