The critical group of $C_4\times C_n$

TL;DR

This paper determines the structure of the critical group for the Cartesian product of a 4-cycle and an n-cycle graph, providing insights into its algebraic properties.

Contribution

It explicitly computes the critical group structure of the graph $C_4 imes C_n$, a problem previously unresolved for this class of graphs.

Findings

Critical group structure of $C_4 imes C_n$ is fully characterized.

Provides formulas for the invariant factors of the critical group.

Enhances understanding of algebraic properties of Cartesian product graphs.

Abstract

In this paper, the critical group structure of the Cartesian product graph $C_4\times C_n$ is determined, where $n\ge 3$.