The notion of a C-ultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and then a strongly connected ~ C4-ultrahomogeneous oriented graph on 168 vertices and 126 pairwise arc-disjoint 4-cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, by altering a definition of the Coxeter graph via pencils of ordered lines of the Fano plane in w...

We present characterizations of connected graphs G of order n ≥ 2 for which h + (G) = n. It is shown that for every two integers n and m with 1 ≤ n − 1 ≤ m ≤ n 2 , there exists a connected graph G of order n and size m such that for each integer k with 2 ≤ k ≤ n, there exists an orientation of G with hull number k. 1. Introduction. The (directed) distance d(u, v) from a vertex u to a vertex v i...

Many applications, from everyday file system browsers to visual programming tools, require the display of network and graph structures. The Graph Visualization Framework (GVF) is an architecture that supports the tasks common to most graph browsers and editors. This article gives a brief overview of the design of the GVF and focuses on the core classes that are used to represent and manipulate ...

We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case when G is regular of degree k, we show that the sandpile group of G is isomorphic to the quotient of the sandpi...

The excess of a graph G is defined as the minimum number of edges that must be deleted from G in order to get a forest. We prove that every graph with excess at most k has chromatic number at most 1 2(3+ √ 1 + 8k) and that this bound is tight. Moreover, we prove that the oriented chromatic number of any graph with excess k is at most k+3, except for graphs having excess 1 and containing a direc...

Oriented ribbon graphs (dessins d’enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram L , there is an associated ribbon graph whose quasi-trees correspond bijectively to spanning trees of the graph obtained by checkerboard coloring L . This corresp...

We prove that for all ` ≥ 3 and β > 0 there exists a sparse oriented graph of arbitrarily large order with oriented girth ` and such that any 1/2+β proportion of its arcs induces an oriented cycle of length `. As a corollary we get that there exist infinitely many oriented graphs with vanishing density of oriented girth ` such that deleting any 1/`-fraction of their edges does not destroy all t...

In this paper we will describe our approach, based on Graph Rewriting (GR), to support the visual modeling process in Tropos, an Agent Oriented software engineering methodology. We will give examples of the rewriting rules which specify the syntax of Tropos and will discuss how this graph rewriting rule-set can support an analyst in building correct models (that is models consistent with the Tr...

Fujaba supports the visual modeling of software applications and the generation of according Java code. During its execution, the runtime state of the generated applications can be saved and restored using the CoObRA framework. In this paper, we present the graph-oriented database DRAGOS for the persistent storage as alternative to CoObRA. Due to the extensive functionality of DRAGOS, the datab...

The agent paradigm can be seen as an extension of the notion of (active) objects by concepts like autonomy, cooperation, and goal-oriented behavior. Mainstream object-oriented modeling techniques do not account for these agentspecific aspects. Therefore, dedicated techniques for agent-oriented modeling are required which are based on the concepts and notations of object-oriented modeling and ex...