Characteristic polynomials of digraphs having a semi-free action

✍ Scribed by Aiping Deng; Yaokun Wu

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 322 KB
• Volume: 408
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2005.06.016

✦ Synopsis

Let φ be a semi-free action of a group G on a finite digraph . The front divisor /π(φ) of has as vertex set the set of the vertex orbits of φ and there are t arcs going from ū to v in /π(φ) if from any vertex u of the orbit ū there are t arcs of going towards the vertices in v. Our main result is that the characteristic polynomial of is a product of the characteristic polynomial of its front divisor /π(φ) and polynomials associated with the free part of under φ. This work extends earlier work of Lee and Kim [Characteristic polynomials of graphs having a semifree action, Linear Algebra Appl. 307 (2000) 35-46].