Theories of graphs and graph transformations form an important part of the mathematical foun-dations of computing, and have been applied in a wide range of areas from the design and analysisof algorithms to the formalization of various computer systems and programs. In this thesis, westudy how graphs and graph transformations can be used to model the static structure and dynamic...

We present an algorithm which takes a graph as input and decides in polynomial time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algorithm returns the set of signed cocircuits of the oriented matroid.

A dominating set of an oriented graph D is a set S of vertices of D such that every vertex not in S is a successor of some vertex of S. The minimum cardinality of a dominating set of D, denoted γ(D), is the domination number of D. An irredundant set of an oriented graph D is a set S of vertices of D such that every vertex of S has a private successor, that is, for all x ∈ S, |O[x]− O[S − x]| ≥ ...

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

A strong oriented k-coloring of an oriented graph G is a homomorphism φ from G to H having k vertices labelled by the k elements of an abelian additive group M , such that for any pairs of arcs −→ uv and −→ zt of G, we have φ(v)−φ(u) 6= −(φ(t)−φ(z)). The strong oriented chromatic number χs(G) is the smallest k such that G admits a strong oriented k-coloring. In this paper, we consider the follo...

The oriented chromatic number o(H) of an oriented graph H is defined to be the minimum order of an oriented graph H ' such that H has a homomorphism to H' . If each graph in a class ~ has a homomorphism to the same H' , then H ' is ~-universal. Let ~k denote the class of orientations of planar graphs with girth at least k. Clearly, ~3 ~ ~4 ~ ~5... We discuss the existence of ~k-universal graphs...