The critical group of $K_m\times C_n$

TL;DR

This paper determines the structure of the critical group for the Cartesian product of a complete graph and a cycle, specifically for graphs of the form $K_m\times C_n$ with $m, n\ge 3$, advancing understanding of algebraic graph invariants.

Contribution

It provides a complete characterization of the critical group structure for the graph $K_m\times C_n$, a problem previously unresolved for these graph classes.

Findings

Critical group structure explicitly determined for $K_m\times C_n$

Results applicable for all $m, n\ge 3$

Enhances understanding of algebraic invariants of product graphs

Abstract

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