Wepropose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set ...

We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors’ opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updat...

We present and investigate a general model for inhomogeneous random digraphs with labeled vertices, where the arcs are generated independently, and the probability of inserting an arc depends on the labels of its endpoints and its orientation. For this model the critical point for the emergence of a giant component is determined via a branching process approach. key words: inhomogeneous digraph...

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

Using the two-way distance, we introduce concept of weak metric dimension a strongly connected digraph [Formula: see text]. We first establish lower and upper bounds for number arcs in text] by using diameter text], characterize all digraphs attaining or bound. Then study with 1 classify vertex-transitive having 1. Finally, order n are determined.

We give a randomized (Las-Vegas) parallel algorithm for computing strongly connected components of a graph with n vertices andm edges. The runtime is dominated byO(log n) multi-source parallel reachability queries; i.e. O(log n) calls to a subroutine that computes the union of the descendants of a given set of vertices in a given digraph. Our algorithm also topologically sorts the strongly conn...

Suppose G is a strongly connected digraph with order n girth g and diameter d. We prove that d + g ≤ n if G contains no arcs (u, v) with deg(u) = 1 and deg(v) ≤ 2. Caccetta and Häggkvist showed in 1978 that any digraph of order n with minimum outdegree 2 contains a cycle of length at most dn/2e. Applying the abovementioned result, we improve their result by replacing the minimum outdegree condi...

Eilers et al. have recently completed the geometric classification of unital graph $C^\ast$-algebras up to Morita equivalence using a set moves on corresponding digraphs. We explore question whether these preserve nonzero elements spectrum finite digraph, which in this paper is allowed loops and parallel edges. consider several different digraph spectra that been studied literature, answering f...

A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. This defines an equivalence relation where two digraphs are equivalent if one can be obtained from the other by a sequence of such operations. We show that given an adjacency-list representation of a digraph G, many fundamental graph algorithms can be carried out on any...

Given a digraph D on n vertices, a matrix A of size n is said to have pattern D, if it has entry Aij 6= 0 if and only if (vi, vj) is an arc of D. We give a necessary condition, which is called strong quadrangularity, for a digraph to be the pattern of a unitary matrix. With the use of such a condition, we show that a line digraph L (D) is the pattern of a unitary matrix if and only if D is Eule...