Abstract
In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In these studies, degree-based topological indices have a significant place among the other descriptors because of the ease of generation and the speed with which these computations can be accomplished. In this paper, we give the results related to the first, second, and third Zagreb indices, forgotten index, hyper Zagreb index, reduced first and second Zagreb indices, multiplicative Zagreb indices, redefined version of Zagreb indices, first reformulated Zagreb index, harmonic index, atom-bond connectivity index, geometric-arithmetic index, and reduced reciprocal Randić index of a new graph operation named as “subdivision vertex-edge join” of three graphs.
Highlights
In mathematical chemistry and chemical graph theory, a topological index is a numerical criterion that is computed based on the molecular graph of a chemical structure
It is important to know which physico-chemical properties are carried from original graphs to the newly constructed graph via this new operation
The present section provides the results related to the first, second, and third Zagreb indices, forgotten index, hyper Zagreb index, reduced first and second Zagreb indices, multiplicative Zagreb indices, redefined version of Zagreb indices, first reformulated Zagreb index, harmonic index, atom-bond connectivity index, geometric-arithmetic index, and reduced reciprocal Randić index of the subdivision vertex-edge join of three graphs
Summary
In mathematical chemistry and chemical graph theory, a topological index is a numerical criterion that is computed based on the molecular graph of a chemical structure. There are several studies regarding TIs of different graph operations (see, e.g., [26,27,28,29,30,31,32]) Very recently, another graph operation, named as the subdivision vertex-edge join (SVE-join), has been introduced [33]. In 1972, Gutman and Trinajstić [1] introduced the first Zagreb index based on the degree of vertices of Z. The first and second Zagreb indices of a graph Z can be defined in the following way:. Inspired by the first and second Zagreb indices, Furtula and Gutman [36] proposed the forgotten topological index (or F-index) of Z in the following way:. Many molecular characteristics of newly formed compound via this operation can be predicted by computing the expression for their additive degree-based indices
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