Platt index

Platt introduced18> an index F which is calculated by summation of the number of bonds adjacent to each of the bonds in the molecule. In graph-theoretical terms, the Platt index is the sum of the degrees of all edges in the molecular graph ... 

The Platt index is defined by using the adjacency matrix of edges, exactly in the same way in which the index of vertex total adjacency, A, was defined (i.e., eqns. 1 and 6). Hence, it could be called edge total adjacency. Otherwise, the indices A and F are called vertex and edge first neighbour sum. The Platt index was used 18) in correlations with some molecular properties in conjunction with other topological indices. 

Those derived from the adjacency matrix the total adjacency index, the Zagreb group indices, the Randic connectivity index, the Platt index, the compatibility code, and the largest eigenvalue index ... 

In the same simple distance- (path) or degree-based category we may recall the Harary index (Hal) Harary (1969), defined as half-sum of the off-diagonal elements of the reciprocal molecular distance matrix of the molecule, as well as the Platt index (Pal) computed as the sum of the edge degrees of a molecular graph (Platt, 1952). 

The total edge adjacency index Ae (also known as Platt number, F [Platt, 1947 Platt, 1952]) is the sum over all entries of the edge adjacency matrix ... 

Although several molecular quantities were defined from the beginiming of quantum chemistry and graph theory, the term molecular descriptor has become popular with the development of structure-property correlation models. The - Platt number [Platt, 1947] and - Wiener index [Wiener, 1947c], defined in 1947, are sometimes referred to as the first molecular descriptors. 

Platt number total edge adjacency index -> edge adjacency matrix PLS-based variable selection - variable selection P matrix -> bond order indices (O graphical bond order)... 

Based on the graph theory, the Wiener index [Wiener, 1947c Wiener, 1947a Wiener, 1947b] and the -+ Platt number [Platt, 1947] are the first - theoretical molecular descriptors proposed in 1947 to model the boiling point of hydrocarbons. 

The two Zagreb indices are strictly related to zero-order °x and first-order - connectivity indices, respectively. The 1 Zagreb index M (also called Gutman index) is also related to the - Platt number F and the - connection number Na by the relationship ... 

The sum of the entries of the matrix S coincides with the —> Platt number F and twice the —> Gordon-Scantlebury index Nqs ... 

Platt number = total edge adjacency index —> edge adjacency matrix... 

This is derived from the partition of edge adjacency matrix elements according to their magnitude and is a trivial quantity because the zero entries do not contribute to the total edge adjacency index Ag ( Platt number), that is, the sum of all elements of the edge adjacency matrix, corresponding to tv ice the connection number N2 ... 

The lowest level structure descriptor is simply the count of atoms. However, only in alkanes are the properties even roughly proportional to the number of atoms. More information-rich structure indicators are needed. In the earliest topological methods, numerical indexes were developed simply by counting the number of edges or pairs of adjacent edges. Wiener,Platt,and others " developed structure indexes that produced interesting correlations to some properties of saturated hydrocarbons. As impressive as this work is, it could not be readily or usefully extended to unsaturated compounds or to heteroatom-... 

Braveman RM, Lebowitz RL (1991) Occult ectopic ureter in girls diagnosis with CT. AJR 156 365-366 Bude RO, DiPietro MA, Platt JE et al (1992) Age dependency of the renal resistive index in healthy children. Radiology 184 469-473... 

---