The Global Cyclicity Index of Benzenoid Chains

Abstract EN

The resistance distance ΩG(i,j) between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor.

The conductance excess between any i and j of G is the difference between 1/ΩG(i,j) and the reciprocal of the distance between i and j.

The global cyclicity index of G is defined as the sum of conductance excesses between all pairs of adjacent vertices.

In this paper, by computing resistance distances between pairs of adjacent vertices in linear polyacenes, an explicit formula for the global cyclicity index of a benzenoid chain is obtained in terms of its number of hexagons.