New isomerization operations for fullerene graphs

The problem of topological isomerization operations for fullerenes is considered. Two basic classes of isomerization transformations admissible for fullerene graphs are proposed: rotation and mirror reflection of a chosen part of fullerene graph. Pyracylene and generalized Stone-Wales rearrangements are only the specific cases of extended isomerization operations for the fullerene graphs.     

Scalable distance similarity of chemical structures

Screening a library of molecular graphs for an exact or approximate match with one particular molecular graph, the query graph, is reduced to list comparisons. The lists contain lengths of shortest paths in graph Voronoi regions. This induces the notion of shortest path similarity. All graphs that are shortest path similar to the query graph are efficiently retrievable. The same applies to approximate or similarity matching. For the retrieval of all superstructures of a query, shortest path lists are modified to distance patterns. This also allows algorithmic support for query construction.     

On the centrality of vertices of molecular graphs

For acyclic systems the center of a graph has been known to be either a single vertex of two adjacent vertices, that is, an edge. It has not been quite clear how to extend the concept of graph center to polycyclic systems. Several approaches to the graph center of molecular graphs of polycyclic graphs have been proposed in the literature. In most cases alternative approaches, however, while being apparently equally plausible, gave the same results for many molecules, but occasionally they differ in their characterization of molecular center. In order to reduce the number of vertices that would qualify as forming the center of the graph, a hierarchy of rules have been considered in the search for graph centers. We reconsidered the problem of “the center of a graph” by using a novel concept of graph theory, the vertex “weights,” defined by counting the number of pairs of vertices at the same distance from the vertex considered. This approach gives often the same results for graph centers of acyclic graphs as the standard definition of graph center based on vertex eccentricities. However, in some cases when two nonequivalent vertices have been found as graph center, the novel approach can discriminate between the two. The same approach applies to cyclic graphs without additional rules to locate the vertex or vertices forming the center of polycyclic graphs, vertices referred to as central vertices of a graph. In addition, the novel vertex “weights,” in the case of acyclic, cyclic, and polycyclic graphs can be interpreted as vertex centralities, a measure for how close or distant vertices are from the center or central vertices of the graph. Besides illustrating the centralities of a number of smaller polycyclic graphs, we also report on several acyclic graphs showing the same centrality values of their vertices. © 2013 Wiley Periodicals, Inc.     

Similarity searching using reduced graphs

Reduced graphs provide summary representations of chemical structures. In this work, the effectiveness of reduced graphs for similarity searching is investigated. Different types of reduced graphs are introduced that aim to summarize features of structures that have the potential to form interactions with receptors while retaining the topology between the features. Similarity searches have been carried out across a variety of different activity classes. The effectiveness of the reduced graphs at retrieving compounds with the same activity as known target compounds is compared with searching using Daylight fingerprints. The reduced graphs are shown to be effective for similarity searching and to retrieve more diverse active compounds than those found using Daylight fingerprints; they thus represent a complementary similarity searching tool.     

计算机自动结构解析专家系统研究──一个新的拓扑等价性识别算法

介绍了一个正确识别化合物结构或结构片断中各原子的拓扑等价性问题的新算法。算法中引入了节点矩阵Ｎ和键矩阵Ｂ，并由这两个新矩阵来计算化合物结构图中的各节点的特征值，以此来表征节点的环境特征，从而识别节点的拓扑等价性，以保证结构解析专家系统结构产生器的穷举和非冗余性。     

Similarity searching in databases of flexible 3D structures using smoothed bounded distance matrices

This paper describes a method for calculating the similarity between pairs of chemical structures represented by 3D molecular graphs. The method is based on a graph matching procedure that accommodates conformational flexibility by using distance ranges between pairs of atoms, rather than fixing the atom pair distances. These distance ranges are generated using triangle and tetrangle bound smoothing techniques from distance geometry. The effectiveness of the proposed method in retrieving other compounds of like biological activity is evaluated, and the results are compared with those obtained from other, 2D-based methods for similarity searching.