On neighborhood Zagreb index of product graphs

Abstract

The properties and activities of chemicals are strongly related to their molecular structures. Topological indices defined on these molecular structures are capable to predict those properties and activities. In this article, a new topological index named as neighborhood Zagreb index ( M N ) is presented. Here the chemical importance of the M N index is investigated and it is shown that the newly introduced index is useful in predicting physico-chemical properties with high accuracy compared to some well-established and often used indices. The isomer-discrimination ability of M N is also examined. To demonstrate how the computational formula of the novel index for chemical compounds is simple and convenient, the chemical structures of favipiravir and hydroxychloroquine are used. In addition, some explicit results for this index of different product graphs such as Cartesian, tensor and wreath product are derived. Some of these results are applied to obtain the M N index of some special structures.

Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers

“…The symmetric division degree index is significant to determine the total surface area of polychlorobiphenyls [ 35 ]. In [ 14 , 39 , 40 ], it is established that the descriptors listed in Table 2 exhibit well-predictive ability for the physicochemical properties entropy ( S ) and acentric factor ( AF ) for the diverse data set of octanes (Table 6 ).…”

“…The neighborhood degree sum-based indices under consideration outperform the well-used degree-based indices , , F , R , SCI , and SDD in modeling entropy, acentric factor and molar refraction [ 39 , 40 , 44 , 50 , 51 ]. Also, the considered indices have remarkable isomer discrimination ability in comparison with aforesaid well-known degree-based indices [ 39 , 40 , 44 , 50 , 51 ]. Most of the neighborhood degree sum-based indices have analogous formula to degree-based indices.…”

“…Konstantinova introduced the sensitivity [26] to measure the isomer discrimination ability of molecular descriptors. Supremacy of the aforementioned descriptors compared to other degree-based descriptors in uniquely characterizing the individual molecular graphs is established in [39,40,44,50,51]. It is therefore reasonable computing such descriptors for various chemically important networks and polymer structures.…”

“…In some recent works [ 7 , 69 ], degree-based molecular descriptors for benzenoid systems and graphitic carbon nitride are computed. Inspired by the degree-based indices, present authors have designed some neighborhood degree sum-based indices having good correlations with entropy and acentric factor [ 14 , 39 , 40 ]. They are given in Table 2 .…”

QSPR analysis of some novel neighbourhood degree-based topological descriptors

“…For more study about degree based topological indices, readers are referred to the articles [5,10,24,25,27,32]. Recently, the present authors introduced some new indices [30,31] based on neighborhood degree sum of nodes. As a continuation, we present here some new topological indices, named as first NDe index (ND 1 ), second NDe index (ND 2 ), third NDe index (ND 3 ), fourth NDe index (ND 4 ), fifth NDe index (ND 5 ), and sixth NDe index (ND 6 ) and defined as…”