Graph invariant atom partitioning

ACMF = augmented connectivity molecular formula AIC = atom invariant class CCAP = canonical code generation by automorphism permutation CSR ture representation EC = extented graph invariant atom partitioning ordered extended connectivity ITS structure. 

Many coding algorithms used in chemistry use a combination of cooperative labeling and atom partitioning with a discriminant graph invariant. An algorithm for canonical coding can be separated into two steps ... 

Graph potentials, a new class of atomic invariants defined as the solutions of a system of linear equations, were proposed as an efficient method of atom partitioning. Molecular graph potentials were developed by analogy with an electrical network, where resistors of the network correspond to chemical bonds and the network nodes correspond to atoms, To cause the flow of electrical current in the network, an additional node is introduced and connected with all other nodes of the network by edges containing resistors and current sources. Atom potentials are computed as the roots of the following system of linear equations ... 

This number can be further reduced by the use of more powerful vertex invariants, like the distance sum. The distance sum, DS, of a vertex i is the sum of the topological distances from vertex i to all other vertices in the molecular graph. The partitioning in the DS equivalence classes of atoms from 4-ethyloctane is presented in (10), showing that only two atoms have identical DS values. Using this partitioning, the constitutional symmetry of 4-ethyloctane can be determined with 1 1 1 1 1 1 1 1 2 = 2 permutation labelings. 

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