The Szeged index of power graph of finite groups

Abstract

The Szeged index of a graph is an invariant with several applications in chemistry. The power graph of a finite group G is a graph having vertex set as G in which two vertices u and v are adjacent if v = uᵐ or u = vⁿ for some m, n ∈ N. 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 Zn for any n > 2. We further obtain a relation between the Szeged index of the power graph of Zn and the Szeged index of the power graph of the dihedral group Dn. We also provide SAGE codes for evaluating the Szeged index of the power graph of Zn and Dn at the end of this paper.