The Szeged Index of Power Graph of Finite Groups
Subarsha Banerjee

TL;DR
This paper derives formulas for the Szeged index of power graphs of finite groups, especially cyclic and dihedral groups, and provides computational tools for these indices.
Contribution
It introduces a formula for the Szeged index of the generalized join of graphs and applies it to power graphs of finite cyclic and dihedral groups.
Findings
Szeged index formula for the generalized join of graphs
Explicit Szeged index for power graph of cyclic groups
Relation between Szeged indices of cyclic and dihedral groups
Abstract
The Szeged index of a graph is an invariant with several applications in chemistry. The power graph of a finite group is a graph having vertex set as in which two vertices and are adjacent if or for some . In this paper, we first obtain a formula for the Szeged index of the generalized join of graphs. As an application, we obtain the Szeged index of the power graph of the finite cyclic group for any . We further obtain a relation between the Szeged index of the power graph of and the Szeged index of the power graph of the dihedral group . We also provide SAGE codes for evaluating the Szeged index of the power graph of and at the end of this paper.
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