TOPOLOGICAL ORGANIC-CHEMISTRY .6. GRAPH-THEORY AND MOLECULAR TOPOLOGICAL INDEXES OF CYCLOALKANES

Adjacency (A), distance (D), and degree (v) matrices of representative cycloalkanes were used to generate molecular topological indices derived from the graphs of the cycloalkanes. Invariant indices (descriptors) were derived from the following matrix operations: the sum of the elements of the product of the degree vector and the distance matrix; the sum of the elements of the product of the degree vector and the sum of the adjacency and distance matrices; the determinant of the distance matrix and its principal eigenvalue; the determinant of the sum of the adjacency and distance matrices and its principal eigenvalue; the permanent of the distance matrix; the product of the row sums of the distance matrix; the short and long hafnians of the distance matrix; and the N-iteration value of the adjacency matrix, where N equaled the number of vertices in the graph. One variant index (code) was calculated-the sum of the elements obtained by multiplying the degree and decimalized adjacency vectors.