A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping φ from V (G) to V (H), that is φ(x)φ(y) is an arc in H whenever xy is an arc in G. The oriented chromatic number of G is the minimum order of an oriented graph H such that G has a homomorphism to H . The oriented chromatic index of G is the minimum order of an oriented graph H such that the line-digraph ...

The skew energy of an oriented graph was introduced by Adiga, Balakrishnan and So in 2010, as one of various generalizations of the energy of an undirected graph. Let G be a simple undirected graph, and Gσ be an oriented graph of G with the orientation σ and skew-adjacency matrix S(Gσ). The skew energy of the oriented graph Gσ , denoted by ES(G), is defined as the sum of the norms of all the ei...

An oriented k-coloring of an oriented graph ~ G = (V, ~ E) is a partition of V into k subsets such that there are no two adjacent vertices belonging to the same subset and all the arcs between a pair of subsets have the same orientation. The decision problem k-oriented chromatic number (ocnk) consists of an oriented graph ~ G and an integer k > 0, plus the question if there exists an oriented k...

A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping φ from V (G) to V (H), that is φ(x)φ(y) is an arc in H whenever xy is an arc in G. The oriented chromatic number of G is the minimum order of an oriented graph H such that G has a homomorphism to H. The oriented chromatic index of G is the minimum order of an oriented graph H such that the line-digraph o...

The inseparability graph of an oriented matroid is an invariant of its class of orientations. When an orientable matroid has exactly one class of orientations the inseparability graph of all its orientations is in fact determined by its non-oriented underlying matroid. From this point of view it is natural to ask if inseparability graphs can be used to characterize matroids which have exactly o...

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

In this paper, we describe the implementation of IUGQL, a graph oriented query language for object oriented databases that is based on the Graph Oriented Object Data (GOOD) model. In the implementation, databases (graphs) are represented as a set of (named) binary relations. The graph oriented queries are translated into equivalent Tarski algebra expressions. These Tarski expressions manipulate...

An oriented k-coloring of an oriented graph G is a mapping c : V (G) → {1, 2, . . . , k} such that (i) if xy ∈ E(G) then c(x) 6= c(y) and (ii) if xy, zt ∈ E(G) then c(x) = c(t) =⇒ c(y) 6= c(z). The oriented chromatic number ~ χ(G) of an oriented graph G is defined as the smallest k such that G admits an oriented k-coloring. We prove in this paper that every Halin graph has oriented chromatic nu...

We classify the countably infinite oriented graphs which, for every partition of their vertex set into two parts, induce an isomorphic copy of themselves on at least one of the parts. These graphs are the edgeless graph, the random tournament, the transitive tournaments of order type ωα, and two orientations of the Rado graph: the random oriented graph, and a newly found random acyclic oriented...

A graph is planar if it can be embedded on the plane without edge-crossing. A graph is 2-outerplanar if it has a planar embedding such that the subgraph obtained by removing the vertices of the external face is outerplanar (i.e. with all its vertices on the external face). An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that eve...