A new general molecular coding Prolog program is used in theoretical studies of the properties of fullerene isomers and derivatives to identify the topological equivalence classes of atoms and bonds in C20-C60 fullerenes. The symmetry perception algorithm is based on an exhaustive search of a minimal code. During this search all canonical labeled mapping trees are generated, allowing constructi...

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 ...

Given an (un)directed connected graph G = (V; E) as a set of edges, let ?(v) be the set of neighbors of a vertex v 2 V. We show that the equivalence-relation R with uRv :, ?(u) = ?(v) on the vertices of the graph can be computed in linear time and space. Many problems can be solved on the graph G induced by the equivalence-classes and the result extended to G. An example for this is the all-pai...

10 The question of efficient characterization of inclusion neighbourhood is crucial in some 11 methods for learning (equivalence classes of) Bayesian networks. In this paper, neighbouring 12 equivalence classes of a given equivalence class of Bayesian networks are characterized effi13 ciently in terms of the respective essential graph. One can distinguish two kinds of inclusion 14 neighbours: u...

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, if P(G) = P(H). A set of graphs S is called a chromatic equivalence class if for any graph H that is chromatically equivalent with a graph G in S, then H ∈S. Peng et al. (Discrete Math. 172 (1997) 103–114), studied the chromatic equivalence classes of certain generalized polygon trees. In thi...

A behavior-RTL equivalence checking method based on bottom-up reasoning is presented. Behavior and RTL descriptions are converted into dependence graphs from which virtual controllers/datapaths are generated. Actual equivalence checking is based on isomorphism analysis on dependence graphs and also virtual controllers/datapaths. First equivalence classes on partial computations are extracted by...

As previously known, all 3-manifolds of genus 2 can be represented by edgecoloured graphs uniquely defined by 6-tuples of integers satisfying simple conditions. The present paper describes an elementary transformation on these 6-tuples which changes the associated graph but does not change the represented manifold. This operation is a useful tool in the classification problem for 3-manifolds of...

As previously known, all 3-manifolds of genus two can be represented by edge-coloured graphs uniquely defined by 6-tuples of integers satisfying simple conditions. The present paper describes an “elementary transformation” on these 6-tuples which changes the associated graph but does not change the represented manifold. This operation is a useful tool in the classification problem for 3-manifol...