Abstract
The general sum-connectivity index is a molecular descriptor defined as chi_{alpha}(X)=sum_{xyin E(X)}(d_{X}(x)+d_{X}(y))^{alpha}, where d_{X}(x) denotes the degree of a vertex xin X, and α is a real number. Let X be a graph; then let R(X) be the graph obtained from X by adding a new vertex x_{e} corresponding to each edge of X and joining x_{e} to the end vertices of the corresponding edge ein E(X). In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph L(X) and rooted product of graphs.
Highlights
Topological indices are useful tools for theoretical chemistry
Topological indices related to their use in quantitative structure-activity (QSAR) and structure-property (QSPR) relationships are very interesting
In the QSAR/QSPR study, physico-chemical properties and topological indices such as the Wiener index, the Szeged index, the Randić index, the Zagreb indices and the ABC index are used to predict the bioactivity of the chemical compounds
Summary
Topological indices are useful tools for theoretical chemistry. A structural formula of a chemical compound is represented by a molecular graph. The atoms of the compounds and chemical bonds represent the vertices and edges of the molecular graphs, respectively. Topological indices related to their use in quantitative structure-activity (QSAR) and structure-property (QSPR) relationships are very interesting. A single number that characterizes some properties corresponding to a molecular graph represents a topological index. All topological indices are useful in different fields, but degree-based topological indices play an important role in chemical graph theory and in theoretical chemistry. The degree of a vertex x ∈ V (X) is the number of vertices adjacent to x and represented by dX(x) = NX(x). The maximum and minimum vertex degree of X are denoted by X and δX , respectively. In the chemical and mathematical literature, several dozens of vertex-based graph invariants have been considered, in hundreds of published papers.
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