Original scientific paper

On Reciprocal and Reverse Balaban Indices

Bo Zhou orcid.org/0000-0001-7321-9554 ; Department of Mathematics, South China Normal University, Guangzhou 510631, China
Nenad Trinajstić ; The Rugjer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia

Abstract

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, M_i is the i-th row sum of M and the summation goes over all edges from the edge-set E(G). Here we consider the reciprocal Balaban index rJ(G)=J(RD, G) and the reverse Balaban index rJ_r(G)=J(RW, 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.

Keywords

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

Hrčak ID:

39680

URI

https://hrcak.srce.hr/39680

Publication date:

15.7.2009.

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