In this article, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time algorithm proposed. It shown that the error system of proposed can be decomposed into group individual passive (IFP) systems interact with each other using output feedback information. Based on IFP framework, convergence conditions suit...

In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of those cuts. We give a conditional lower bound that provides evidence that our algorithms may be tight up to a sub-polynomial factors. As an additional resul...

two digraphs of same order are said to be skew-equienergetic if theirskew energies are equal. one of the open problems proposed by li andlian was to construct non-cospectral skew-equienergetic digraphs onn vertices. recently this problem was solved by ramane et al. inthis paper, we give some new methods to construct new skew-equienergeticdigraphs.

Let D s (n; h, d = k) denote the number of h-strongly connected digraphs of order n and diameter equal to k. In this paper it is shown that: i) Ds(n; 11" d = 3) = 4(~) (3/4 + o(I))n for every fixed h ;::: 1; ii) Ds(n; h, d = 4) = 4(~) (2h 2 + 2-2 + o(I))n for every fixed h ;::: 2; iii) Ds(n; 11" d = k) = 4(~) ((2h+l I)2-kh+:3h-2 + o(I))n for every fixed h ;::: 1 and k ;::: 5. Similar asymptotic...

Let G be a directed graph and G be its r-th power. We study different issues dealing with the number of arcs, or size, of G and G: given the order and diameter of a strongly connected digraph, what is its maximum size, and which are the graphs achieving this bound? What is the minimum size of the r-th power of a strongly connected digraph, and which are the graphs achieving this bound? Given al...

This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.