Hamiltonian Cycles for Finite Weyl Groupoids

Abstract

Let $Γ({\mathcal{W}})$ be the Cayley graph of a finite Weyl groupoid ${\mathcal{W}}$. In this paper, we show an existence of a Hamitonian cycle of $Γ({\mathcal{W}})$ for any ${\mathcal{W}}$. We exatctly draw a Hamiltonian cycle of $Γ({\mathcal{W}})$ for any (resp. some) irreducible ${\mathcal{W}}$ of rank three (resp. four). Moreover for the irreducible ${\mathcal{W}}$ of rank three, we give a second largest eigenvalue of the adjacency matrix of $Γ({\mathcal{W}})$, and know if $Γ({\mathcal{W}})$ is a bipartite Ramanujan graph or not.

Theorems & Definitions (50)

• Definition 1.1
• Theorem 1.2
• Theorem 1.3
• Definition 2.1
• Definition 2.2
• Definition 2.3
• Lemma 2.4
• Proposition 2.5
• Lemma 2.6
• proof