Basic subgraphs

A tremendous number of various fragments are used in structure-property studies atoms, bonds, topological torsions , chains, cycles, atom- and bond-centered fragments, maximum common substructures, line notation (WLN and SMILES) fragments, atom pairs and topological multiplets, substituents and molecular frameworks, basic subgraphs, etc. Their detailed description is given below. 

Another application of basic subgraphs arises from the possibility of relating the invariants of molecular graphs to the occurrence numbers of some basic subgraphs. Estrada has developed this methodology for spectral moments of the edge-adjacency matrix of molecular graphs - defined as the traces of the different powers of such matrix ... 

The refinement procedure utilises the fact that if some query node Q(X) has another node Q(fV) at some specific distance ) ( and/or angle), and if some database node D(Z) matches with Q(W), then there must also be some node D(Y) at the appropriate distance(s) from D(Z) which matches with Q(X) this is a necessary, but not sufficient, condition for a subgraph isomorphism to be present (except in the limiting case of all the query nodes having been matched, when the condition is both necessary and sufficient). The refinement procedure is called before each possible assignment of a database node to a query node and the matched substructure is increased by one node if, and only if, the condition holds for all nodes W, X, Y and Z. The basic algorithm terminates once a match has been detected or until a mismatch has been confirmed [70] it is easy to extend the algorithm to enable the detection of all matches between a query pattern and a database structure, as is required for applications such as those discussed here. 

Intrinsically non-planar graphs are non-planar by virtue of their connectivity only. It has been shown [51] that they all contain one of the two basic non-planar graphs as a subgraph [60] the first and the second Kuratowski graphs K5 and... 

Overall connectivity indices vere proposed as a meaningful measure of topological complexity of molecules, since they satisfy two fundamental requirements to a complexity measure to increase with both the number of structural elements and their intercoimectedness the basic idea is that The higher the connectivity of molecular graph and its connected subgraphs, the more complex the molecule [Bonchev and Trinajstic, 1977]. 

Procedures are supported in the VT by grouping a set of basic blocks into a subgraph called a vtbody. A vtbody is a graph that is translated from an ISPS procedure or labelled block. Values from surrounding code that are used in the ISPS procedure become explicit data-flow inputs to the graph. Similarly, values that are produced in the procedure and referenced in the surrounding code become explicit data-flow outputs of the vtbody graph. 

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