Comprehensive interpretation of hand-drawn diagrams is a long-standing challenge. Connectors (arrows, edges and lines) are important components of many types of diagram. In this paper we discuss techniques for syntactic and semantic recognition of connectors. Undirected graphs, digraphs and organization charts are presented as exemplars of three broad classes that encompass many types of connec...

For a local tournament D with minimum out-degree δ, minimum indegree δ− and irregularity ig(D), we give a lower bound on the connectivity of D, namely κ(D) ≥ (2 ·max{δ+, δ−}+ 1− ig(D))/3 if there exists a minimum separating set S such that D − S i is a tournament, and κ(D) ≥ (2 ·max{δ+, δ−}+ 2|δ+ − δ−|+ 1− 2ig(D))/3 otherwise. This generalizes a result on tournaments presented by C. Thomassen [...

The concept of a consecutive-d digraph was proposed by Du, Hsu and Hwang as a generalization of de Bruijn digraphs, Kautz digraphs, and their generalizations given by Imase and Itoh and Reddy, Pradhan and Kuhl. In this paper we determine the connectivity of consecutive-d digraphs and study how to modify consecutive-d digraphs to reach maximum connectivity. Our results will generalize and improv...

Tournaments are without doubt the best studied class of directed graphs [3, 6]. The generalizations of tournaments arise in order to extend the well-known results on tournaments to more general classes of directed graphs. Moreover, the knowledge about generalizations of tournaments has allowed to deepen our understanding of tournaments themselves. The semicomplete digraphs, the semicomplete mul...

Among unicyclic digraphs and signed digraphs with fixed number of vertices, the digraphs and signed digraphs with minimal and maximal energy are already determined. In this paper we address the problem of finding bicyclic signed digraphs with extremal energy. We obtain minimal and maximal energy among all those n -vertex bicyclic signed digraphs which contain vertex-disjoint signed directed cyc...

4 We prove that the weak k-linkage problem is polynomial for every fixed k for totally Φ5 decomposable digraphs, under appropriate hypothesis on Φ. We then apply this and recent results 6 by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence 7 number or bounded cut-width) to get polynomial algorithms for some class of digraphs like quasi8 transitive digraphs...

Relation on a set is simple mathematical model to which many real-life data can be connected. A binary relation always represented by digraph. Topology generated relations the . In this direction, study will consider different classical categories of topological spaces whose topology defined adjacency and reachability vertex directed graph. This paper analyses some properties these topologies s...

Laplacian dynamics on signed digraphs have a richer behavior than those nonnegative digraphs. In particular, for the so-called "repelling" Laplacians, marginal stability property (needed to achieve consensus) is not guaranteed priori and, even when it holds, does automatically lead consensus, as these Laplacians may loose rank in strongly connected Furthermore, time-varying case, instability ca...

We consider the dihamiltonian decomposition problem for 3-regular graphs. A graph G is dihamiltonian decomposable if in the digraph obtained from G by replacing each edge of G as two directed edges, the set of edges are partitioned into 3 edge-disjoint directed hamiltonian cycles. We suggest some conditions for dihamiltonian decomposition of 3-regular graphs: for a 3-regular graph G, it is diha...

Let G = (V, A) be a digraph with diameter D 6= 1. For a given integer 2 ≤ t ≤ D, the t-distance connectivity κ(t) of G is the minimum cardinality of an x → y separating set over all the pairs of vertices x, y which are at distance d(x, y) ≥ t. The t-distance edge connectivity λ(t) of G is defined similarly. The t-degree of G, δ(t), is the minimum among the out-degrees and in-degrees of all vert...