FULL PAPER Comparative analysis of symmetric division deg index as potentially useful molecular descriptor Boris Furtula 1 | Kinkar Ch. Das 2 | Ivan Gutman 1 1 Faculty of Science, University of Kragujevac, Kragujevac, Serbia 2 Department of Mathematics, Sungkyunkwan University, Suwon, Republic of Korea Correspondence Boris Furtula, Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia. Email: boris.furtula@pmf.kg.ac.rs and Kinkar Ch. Das, Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. Email: kinkardas2003@gmail.com Funding information Ministry of Education, Science and Technological Development of Republic Serbia, Grant Number: 174033; National Research Foundation of the Korean government, Grant Number: 2017R1D1A1B03028642 Abstract There are several dozens of vertex–degree–based (VDB) molecular structure descriptors currently stud- ied and proposed to be used in quantitative structure-property/activity relationships (QSPR/QSAR) researches. Among them, just a couple are recognized as promising and worth of practical applications. One of the newest is the symmetric division deg index (SDD). This article is devoted to a thorough multi- faceted analysis of SDD and its comparison with other VDB topological indices. We show that the applicative potential of SDD is comparable to already well-established VDB structure descriptors. Addi- tionally, some of conducted tests indicate its supremacy over other VDB molecular indices. KEYWORDS atom–bond connectivity index, geometric–arithmetic index, quality of molecular descriptors, sym- metric division deg index, vertex–degree–based indices 1 | INTRODUCTION Modern drug design is unimaginable without engaging quantitative structure-property/activity relationships (QSPR/QSAR) routines. This implies comprehensive employment of molecular structure descriptors. A noticeable place among them belongs to the topological indices. [1–3] These are used for extracting substantial information encompassed by the two-dimensional graphical representations of molecules. Topological indices might be classified into several distinct groups. One of the most investigated and widely used is a group of so-called vertex– degree–based indices (VDB). Some members of VDB indices were conceived at the beginning of the development of QSPR/QSAR approaches to chemistry related problems. Nowadays, there is a legion of such topological descriptors. Roughly one half of these were put forward under the name of “Adriatic indices.” [4] The Adriatic indices were proposed and investigated several years ago in a series of articles. [4–7] Just a few of these have emerged as potentially useful in predicting physico–chemical properties of molecules. [4] The so-called “symmetric division deg index” belongs to this exclusive group. It is defined as SDDðGÞ5 X ij2EðGÞ d i d j 1 d j d i   ; (1) where d i and d j are the degrees of the vertices i and j of the underlying molecular graph G, and where the summation goes over all edges of G. It was claimed [4] that SDD correlates well with the total surface area of polychlorobiphenyls (PCB). Motivated by this single detail, several math- ematically oriented investigations of SDD were undertaken. [8–11] The aim of the present work is to test the physico-chemical applicability of SDD on a much wider empirical basis, and to compare it with other, most often used, VDB topological indices. The extended energy concept was revived recently in Ref. [12]. This quantity is calculated as a sum of absolute values of the eigenvalues of an extended adjacency matrix. A non-zero element in this matrix is defined identically as a summand in Equation 1. So, the SDD index is just the half of the sum of all elements in the extended adjacency matrix. This was another impetus for the present analysis of the SDD index. Int J Quantum Chem. 2018;e25659. https://doi.org/10.1002/qua.25659 http://q-chem.org VC 2018 Wiley Periodicals, Inc. | 1 of 14 Received: 3 February 2018 | Revised: 3 April 2018 | Accepted: 19 April 2018 DOI: 10.1002/qua.25659