The Gordon-Scantlebury Index

This index, N2, is defined as the number of distinct ways in which an acyclic — —C fragment can be superimposed on the hydrogen-depleted molecular graph. The N2 index expresses the number of all paths of length two, P2, in the graph  

The comparison with the F-values given above demonstrates the relation between the Gordon-Scantlebury and the Platt indices  

Proceeding from eqn. (13) and the correspondence between A and F indices, one observes that the index N2 corresponds to A. Hence, the Gordon-Scantlebury index has also the meaning of total edge adjacency of the graph. 

Some simple relationships are also found among N2 (or, F), the vertex degree, Vj, the index Mb and the total adjacency A  

Gutman and Randic 23) proposed an important concept for the comparability of chemical structures. They associated a numerical power sequence to a graph  

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

One can also see that the Gordon-Scantlebury N2 index 19) can similarly be expressed as half the number of distances of length two, but for acyclic graphs only ... 

Two adjacent edges constitute a 2" order path and this subgraph is called connection (or link). The connection number N2, also known as Gordon-Scantlebury index... 

Half-sum of the cube of the adjacency matrix Polarity number number of third neighbors Gordon-Scantlebury index number of second neighbors Number of paths of length /i = 0-10 Balaban s J index based on distance Balaban s J index based on multigraph bond orders Balaban s J index based on relative electronegativities Balaban s 7 index based on relative covalent radii Balaban s information-based indexes on distance sums... 

Ngs) [Gordon and Scantlebury, 1964] or Bertz branching index Bl), is the simplest graph-invariant obtained from the edge adjacency matrix which considers both vertices and edges and is calculated as ... 

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