Commuting involution graphs for $\tilde C_n$

TL;DR

This paper investigates the structure of commuting graphs of involution conjugacy classes in the affine Weyl group of type  C_n, establishing an upper bound on their diameter when connected.

Contribution

It provides a new bound on the diameter of commuting involution graphs in affine Weyl groups of type  C_n.

Findings

Connected graphs have diameter at most n+2

The study advances understanding of involution conjugacy in affine Weyl groups

Provides bounds relevant for algebraic and geometric applications

Abstract

In this article we consider commuting graphs of involution conjugacy classes in the affine Weyl group of type $\tilde C_n$. We show that where the graph is connected the diameter is at most $n+2$.