aDipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, via Amendola 2, 42100 Reggio Emilia, Italy;bDepartment of Mathematics, Iowa State University, Ames, IA 50010, USA
Abstract:
We show that there exists a family of r-regular graphs of arbitrarily large excessive index for each integer r greater than 3. Furthermore, we answer a question in Bonisoli and Cariolaro (2007) 1] showing that all the positive integers can be attained as excessive classes of regular graphs.