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Croatica Chemica Acta, Vol.82 No.2 July 2009. -

The Ivanciuc-Balaban operator of a graph G is defined see full text for definition

where M is its molecular matrix with positive row-sums, m is the number of edges, µ is the cyclomatic number, Mi is the i-th row sum of M and the summation goes over all edges from the edge-set EG. Here we consider the reciprocal Balaban index rJG=JRD, G and the reverse Balaban index rJrG=JRW, G, where RD and RW are respectively the reciprocal distance matrix and the reverse Wiener matrix of G. Various lower and upper bounds for these two types of Balaban-like indices are reported.

Ivanciuc-Balaban operator; Balaban index; reciprocal Balaban index; reverse Balaban index

Author: Bo Zhou - ; Department of Mathematics, South China Normal University, Guangzhou 510631, China Nenad Trinajstić - ; The Rugjer Bo

Source: http://hrcak.srce.hr/


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