The Szeged Index of Power Graph of Finite Groups

2025/10/29 by Banerjee, Subarsha
#05C09 #05C25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.25686

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=u^m 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 \mathbb Z_n for any n>2. We further obtain a relation between the Szeged index of the power graph of \mathbb Z_n and the Szeged index of the power graph of the dihedral group D_n. We also provide SAGE codes for evaluating the Szeged index of the power graph of ℤ_n and D_n at the end of this paper.

Citations

• Mathematical aspects of Wiener index

Related

• Hosoya properties of power graphs over certain groups
• Certain properties of the enhanced power graph associated with a finite group
• The Order Supergraph of the Power Graph of a Finite Group
• The power index of a graph
• On the power graph of a finite group