Everett and Borgatti (1991) have suggested an alternative formulisation of Regular Equivalence (White and Reitz 1983) using similar ideas to classical graph colouring. This fo~ulisation provides a simple representation of regular equivalence without the need to resort to complicated algebraic constructions. In this paper we shall extend the ideas in Everett and Borgatti’s paper to digraphs and ...

We study the computational difficulty of deciding whether two matrices generate equivalent linear codes, i.e., codes that consist of the same codewords up to a fixed permutation on the codeword coordinates. We call this problem Code Equivalence. Using techniques from the area of interactive proofs, we show on the one hand, that under the assumption that the polynomial-time hierarchy does not co...

The Shannon capacity of every induced subgraph of a perfect graph equals its clique number. However, for the co{normal powers of an odd cycle the super{multiplicativity of the clique number makes the determination of capacity one of the hardest problems in combinatorics. We study the asymptotic growth of induced subgraphs of some particular type in powers of a xed graph. In case of a simple gra...

Circular planar graphs are used to model electrical networks, which arise in classical physics. Associated with such a network is a network response matrix, which carries information about how the network behaves in response to certain potential differences. Circular planar graphs can be organized into equivalence classes based upon these response matrices. In each equivalence class, certain fu...

Graph dynamical systems (GDSs) generalize concepts such as cellular automata and Boolean networks and can describe a wide range of distributed, nonlinear phenomena. Two GDSs are cycle equivalent if their periodic orbits are isomorphic as directed graphs, which captures the notion of having comparable long-term dynamics. In this paper, we study cycle equivalence of GDSs in which the vertex funct...

We consider the problem of checking equivalence of conjunctive queries with inequalities under bag (multiset) semantics. The problem is known to be decidable in pspace and as hard as graph isomorphism, but its exact complexity remains open. We introduce a natural restriction based on what we call the symmetry degree of queries, and show that when the symmetry degree is bounded by a fixed polyno...

In this paper we develop the theory of train track maps on graphs groups. Expanding a definition Bass, define notion map graph groups, and homotopy equivalence. We prove that under one two technical hypotheses, any equivalence groups may be represented by relative map. The first applies in particular to with finite edge while second certain generalized Baumslag-Solitar

This paper is concerned with redundancy detection and elimination in databases via the solution of a key equivalence problem. The approach is related to the hardening of soft databases method due to Cohen et al., [4]. Here, the problem is described in graph theoretic terms. An appropriate optimization model is drawn and solved indirectly. This approach is shown to be effective. Computational re...

We study the equivalence relation on the set of acyclic orientations of an undirected graph Γ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in tur...

The question of efficient characterization of inclusion neighbourhood is crucial in some methods for learning (equivalence classes of) Bayesian networks. In this paper, neighbouring equivalence classes of a given equivalence class of Bayesian networks are characterized efficiently in terms of the respective essential graph. One can distinguish two kinds of inclusion neighbours: upper and lower ...