Subgraphs

For database handling it is necessary to compare existing database entries with new ones. Consequently, database registration and retrieval are dependent on isomorphism algorithms which compare two graphs or structure diagrams to determine whether subgraphs are identical or not. 

Gq is a substructure of Gp (i.e., Gq is isomorphic with a subgraph of Gp) if and only if all the atoms of Gq can be mapped onto a subset of atoms of Gp in such a way that the bonds of Gq map the corresponding bonds which connect the mapped atoms fi om Gp Each mapping between Gq and Gxcan be considered as a function... 

Figure 6-2. Mappings between the que7 graph (Cq) and the target graph (Cr). Notation such as (2, 1, 3, 4) means that atom 2 of the que subgraph Gq is mapped to atom 1 from the target graph Cp...

A spanning tree in G is an edge-subgraph of G which has N — 1 edges and contains no circuits. 

We arrive at equation (5.106) by applying this result to all principal minors (each of which is the determinant of a subgraph of of size i ).B... 

Category 1 Initial states decay into structurally much simpler final states in which most links have been destroyed so that the graph G consists essentially of a large number of small local subgraphs. 

HarF56 Harary, F. On the number of dissimilar line-subgraphs of a given graph. Pacific J. Math. 6 (1956). 

Strong operator convergence, 616 Sturm sequence, 77 Subgraph, 256 maximal connected, 256 Subgroup decomposition of point groups, 738... 

Raymond JW, Willett P. Maximum common subgraph isomorphism algorithms for the matching of chemical structures. J Comput-Aided Mol Des 2002 16 521-33. 

At the end of this three-step procedure we have generated a graph (i.e., a subgraph of the process graph) whose edges indicate the flow of species Jt, and whose nodes contain the chemical jc, at the given operating state. 

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