Subgraph addition

The figures are annotated and little additional comment is required. Figure 4 illustrates retrieval of a structure and its supergraphs and subgraphs. Figure 5 illustrates reaction retrieval. 

Call a polycycle proper if it is apartial subgraph of r, q) and a helicene, otherwise (this term will be justified later by Theorem 4.3.1). Call a proper (r, )-polycycle induced (moreover, isometric) if this subgraph is, in addition, an induced (moreover, isometric) subgraph of r, q). Another interesting possible property of aptoper (r, q)-polycycle is being convex in r, q (see Section 4.4). 

Now we consider another natural notion of maximality for polycycles. An (r, q)-polycycle is called rum-extensible if it is not a partial subgraph of any other (r, extensible polycycles are helicenes. It is also clear that any 3-connected (r, 3)-polycycle is non-extensible. 

Given a -+ molecular graph ( , where vertices are labelled by the chemical element of the corresponding atoms, cluster expansion in the additive form is among the group contribution methods expressing a molecular property 0 as a sum of contributions of all the connected subgraphs of Q, i.e. 

Additionally, a new construct for modeling alternative subgraphs [180] is realized. This is a powerful construct to specify multiple alternative correspondence structures in one rule. For example, there are different options to map a process stream to a pipe which contains different types of valves in different order. All these alternatives can be now specified within one rule. Concepts for the parametrization of integration rules will be defined. Parameters can be set at runtime as well as at rule definition time. Figure 7.19 shows an example of a rule with a runtime parameter in combination with a set-valued pattern A column in the simulation model is mapped to a column in the flowsheet, which has a number of column trays each having a port. The parameter n controls the number of trays, that are added to the column it is provided by the user at runtime. Up to now, the parametrization works with attributes occurring in a rule whose values can be retrieved at runtime without user interaction. 

The chi indexes, especially those of higher order, exhibit both additive and constitutive character. Because they are by definition summations, the chi indexes are additive. Also the number of terms in each index summation depends in detail on the molecular structure described by the graph, As shown in Figure 3, the number of contributing subgraphs varies with structure, reflecting the constitutive nature of structure, and, hence, of the chi indexes. Further,... 

There are three additional subgraphs besides isobutane isobutane with an isolated carbon, propane with two isolated carbons, and ethane with three isolated carbons, which occur an odd number of times. All this is strong evidence that the set of subgraphs at right in Figure A4.1 are not the Ulam subgraphs of the graph of 3-methylhexane. 

Proof We will prove by induction. After the first call to procedure IncrementalOffset, the offsets = greater than or equal to 0. Since G/ is a subgraph of the constraint graph G, the assertion holds for r = 1. 

---