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Bounds for the general sum-connectivity index of composite graphs
Shehnaz Akhter1, Muhammad Imran1,2, Zahid Raza3
1School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad, Pakistan.
Abstract:
The general sum-connectivity index is a molecular descriptor defined as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text], and α is a real number. Let X be a graph; then let [Formula: see text] be the graph obtained from X by adding a new vertex [Formula: see text] corresponding to each edge of X and joining [Formula: see text] to the end vertices of the corresponding edge [Formula: see text]. 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 [Formula: see text] and rooted product of graphs.
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