A graph is said to be half-arc-transitive if its automorphism group acts transitively on the set of its vertices and edges but not on the set of its arcs. With each half-arc-transitive graph of valency 4 a collection of the so called alternating cycles is associated, all of which have the same even length. Half of this length is called the radius of the graph in question. Moreover, any two adja...

For a graph G, a detachment operation at a vertex transforms the graph into a new graph by splitting the vertex into several vertices in such a way that the original graph can be obtained by contracting all the split vertices into a single vertex. A graph obtained from a given graph G by applying detachment operations at several vertices is called a detachment of graph G. We consider a detachme...

In this paper we give two equivalent characterizations of the Caucal hierarchy, a hierarchy of infinite graphs with a decidable monadic second-order (MSO) theory. It is obtained by iterating the graph transformations of unfolding and inverse rational mapping. The first characterization sticks to this hierarchical approach, replacing the languagetheoretic operation of a rational mapping by an MS...

A unified and general scheme for detecting the termination of distributed computations is proposed. This scheme uses the encoding of distributed algorithms in form of graph rewriting systems to transform the problem of adding termination detection to a distributed computation into an operation on graph rewriting systems. Various examples are used to illustrate this approach.

Using a newly introduced operation on graphs and its counterpart on graph drawings, we prove the conjecture of Jendrol’ and Ščerbová from 1982 about the crossing number of the Cartesian product K1,m2Pn. Our approach is applicable to the capped Cartesian products of Pn with any graph containing a dominating vertex.

Typical ontology matching applications, such as ontology integration, focus on the computation of correspondences holding between the nodes of two graph-like structures, e.g., between concepts in two ontologies. However, for applications such as web service integration, we need to establish whether full graph structures correspond to one another globally, preserving certain structural propertie...

The cut polytope P,(G) of a graph G is the convex hull of the incidence vectors of all cuts of G; the cut cone C(G) of G is the cone generated by the incidence vectors of all cuts of G. We introduce the operation of collapsing an inequality valid over the cut cone C(K,) of the complete graph with n vertices: it consists of identifying vertices and adding the weights of the corresponding inciden...

Brain-inspired computing structures, technologies, andmethods offer innovative approaches to the future of computing. From the lowest level of neuron devices to the highest abstraction of consciousness, the brain drives new ideas (literally and conceptually) in computer design and operation. This paper interrelates three levels of brain inspired abstractions including intelligence, abstract gra...

Definitions of graph embeddings and graph minors for directed graphs are introduced. For the class of 2-terminal directed acyclic graphs (TDAGs) the definitions coincide, and the class is closed under both operations. The usefulness of the directed embedding operation is demonstrated be characterizing all TDAGs with parallel-width at most $k$, which generalizes earlier characterizations of seri...

Using a newly introduced operation on graphs and its counterpart on graph drawings, we prove the conjecture of Jendrol’ and Ščerbová from 1982 about the crossing number of the Cartesian product K1,m2Pn. Our approach is applicable to the capped Cartesian products of Pn with any graph containing a dominating vertex.