Canonical numbering, stereochemical descriptors, and unique linear notations for polyhedral clusters

Compact molecular codes

“…After deriving the modified connectivity values, one establishes ranks for individual vertices and assigns to them Illustration of the search for the TV-tuple code of a tree: labels 1 -n. Construction of the code is straightforward once labels are known. For the graph of Figure 1, one obtains The above can be contracted by leaving out parentheses and interlacing zeros to 123425637114481259610798109101112 In all, 25 symbols (which Herndon further reduced to 24 by eliminating the leading "1" as redundant). Can we have a shorter code?…”

Topology-based stereochemistry representation

“…This permutation is symbolized by the circular dart sequences, where the end point of a dart x touches the start point of a dart y if and only if p1 maps x onto y. We note a mapping p: X + 1 as a subset of the Cartesian product XX Y In VZ, 4), (4,5), (5,3), (6 7), (7,8), (8,6), (9, lo)> (110, .11), (11, 9)) induces the four circular dart sequences (0, 1, 2), (3,4,5), (6,7,8), and (9, 10, 11) as well as the corresponding circular label sequences (c, a, b), (a, c, d), (6, a, d), and (c, LJ, d), thus representing the oriented faces oft.…”

Extended CAST Coding Method for Exact Search of Stereochemical Structures

“…Some coding methods for three-dimensional chemical structures have been developed and used for structural representation in some chemical software, however, an essential problem of exact search of structures considering configurational and conformational structural environments has been remained. [1][2][3][4][5][6] We reported CAST (CAnonical-representation of STereochemistry) coding method in the previous paper 7,8 . The basic CAST gives canonical codes based on the dihedral angles.…”