The central observation of this paper is that if ǫn random arcs are added to any n-node strongly connected digraph with bounded degree then the resulting graph has diameter O(lnn) with high probability. We apply this to smoothed analysis of algorithms and property testing. Smoothed Analysis: Recognizing strongly connected digraphs is a basic computational task in graph theory. Even for digraphs...

Thomassen proved that there is no degree of strong connectivity which guarantees a cycle through two given vertices in a digraph (Combinatorica 11 (1991) 393-395). In this paper we consider a large family of digraphs, including symmetric digraphs (i.e. digraphs obtained from undirected graphs by replacing each edge by a directed cycle of length two), semicomplete bipartite digraphs, locally sem...

In this paper, we study the synchronization problem in complex dynamic networks of Piece Wise Linear (PWL) systems. PWL systems exhibit multi-scrolls and belong to a special class Unstable Dissipative Systems (UDS). We consider strongly connected digraphs linear diffusive couplings. The regions are computed using concept disagreement vectors, generalized algebraic connectivity network topology,...

The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paperweprovide anupper boundof theHarary index in terms of the vertex or edge connectivity of a graph. We characterize the unique graph with themaximumHarary index among all graphs with a given number of cut vertices or vertex connectivity or edge connectivity. In ad...

We construct for all k ∈ N a k-edge-connected digraph D with s, t ∈ V (D) such that there are no edge-disjoint s → t and t → s paths. We use in our construction “self-similar” graphs which technique could be useful in other problems as well.

This paper introduces a method which provides robust tracking results and accurately segmented object boundaries in short computation time. The first step of the algorithm is to apply a novel edge detector on efficiently calculated color probability maps in an object-specific Fisher color space. The proposed edge detector exploits context information by finding the maximally stable boundaries o...

Given a digraph D, its competition graph has the same vertex set and an edge between two vertices x and y if there is a vertex u so that (x, u) and (y, u) are arcs of D. Motivated by a problem of communications, we study the competition graphs of the special digraphs known as semiorders. This leads us to define a conditions on digraphs called C(p) and C(p) and to study the graphs arising as com...

William F. Klostermeyer Dept. Statistics and Computer Science West Virginia University Morgantown, WV 26506-6330 e-mail: [email protected] ABSTRACT A directed graph operation called pushing a vertex is studied. When a vertex is pushed, the orientation of each of its incident edges is reversed. We consider the problems of pushing vertices so as to produce strongly connected, semi-connected, and acy...