let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

It is shown that the molecular symmetry groups can be obtained as the automorphism groups of edge-weighted Euclidean graphs. Graph theory provides an elegant and natural representation of molecular symmetry. The resulting group expressed in terms of permutations is isomorphic to the permutation-inversion group of Longuet-Higgins or the permutational subgroup in case inversion operations do not ...

IT IS OUR VIEW that labeled directed graph data models (simple, nested, or hypergraphs) can naturally and usefully capture a wide variety of biological data and queries. We believe that development of general purpose graph data management systems (GDMSs) could become major platforms for development of a wide variety of bioinformatics database systems spanning applications from DNA sequences, ch...

Molecular activity prediction is critical in drug design. Machine learning techniques such as kernel methods and random forests have been successful for this task. These models require fixed-size feature vectors as input while the molecules are variable in size and structure. As a result, fixed-size fingerprint representation is poor in handling substructures for large molecules. Here we approa...

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global ...

Let E” be n-dimensional Euclidean space. A molecular space is a family of unit cubes in E”. Any molecular space can be represented by its intersection graph. Conversely, it is known that any graph G can be represented by molecular space M(G) in E” for some n. Suppose that S, and S, are topologically equivalent surfaces in E” and molecular spaces M, and M, are the two families of unit cubes inte...

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