Distance sum

M = net free distance (sum) of spaces between tubes from wall to wall at center of shell circle, in. 

DN2Sy Triplet index from distance matrix, square of graph order ( of nonhydrogen atoms), and distance sum operation y — 1-5... 

The values of these distance sums are given below at each vertex in graphs Gj and G2 ... 

Balaban applied 47a b> a Randic-type formula (7) to distance sums instead of vertices and created thereby the most discriminating (least degenerate) topological index proposed so far ... 

For simple graphs (saturated molecules) q is the number of edges. Averaged distance sums ... 

For multiple edges (unsaturated or aromatic systems) fractional distances are introduced in the distance matrix so that fractional distance sums result on summation if the bond order between vertices i, j is b, then 1/b is the entry in the row/... 

In analogy to B, Balaban and Diudea [12] introduced the regressive distance sum matrix, R, which is derived by substituting ds for v ... 

Balaban Index The Balaban index, J, has been introduced as the average-distance sum defined as the sum of the squares of the reciprocal nonzero distances in D (6,7] ... 

Balaban, A. T., and M. V. Diudea, Real Number Vertex Invariants Regressive Distance Sums and Related Topological Indices. J. Chem. Inf. Comput. Sci., 1993 33 421-428. 

This is certainly much more probable than the assumption of a partial double bond character in order to explain the observed shortening of the Si—F distance (sum of atomic radii Pauling 1.81 A Stevenson and Schomaker 1.69 A obs. 1.54 A). 

The formerly proposed and the most important of this series of topological indices is the Baiaban distance connectivity index J (also called distance connectivity index or average distance sum connectivity). It is one of the most discriminating - molecular descriptors and its values do not increase substantially with molecule size or number of rings it is defined in terms of sums over each ith row of the - distance matrix D, i.e. the vertex distance degree o [Baiaban, 1982 Baiaban, 1983a]. It is defined as ... 

The idea behind these LOVIs is that usually the vertices with the highest distance sums have the lowest vertex degrees, thus enhancing the intramolecular differences [Baiaban, 1994a]. 

The vertex distance degree (or distance number, distance index, distance rank, vei tex distance sum, distance of a vertex) is the row sum a, of the distance matrix D ... 

All these quantities are -> local vertex invariants. High values of the vertex distance sum o are observed for -> terminal vertices while low values for -> central vertices. Moreover, among the terminal vertices, the vertex distance degrees are small if the vertex is close to a branching site and larger if the terminal vertex is far away. 

The reciprocal distance sum RDSi of the i th vertex is a local invariant defined as the sum of the reciprocal distance matrix elements in the i th row ... 

The edge distance degree (or edge distance index, edge distance sum) is the row... 

Note that for acyclic graphs, the path degree layer matrix LPD coincides with the distance sum layer matrix LDS. 

In analogy with the regressive vertex degrees, the regressive distance sums (or regressive incremental distance sums) are local invariants obtained by applying the centrocomplexity operator X, to the distance sum layer matrix LDS [Balaban and Diudea, 1993]. Also in this case, a simplified form of the centrocomplexity operator has been proposed ... 

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