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) showing that all the positive integers can be attained as excessiveclasses of regular graphs.
Graphs of arbitrary excessive class / Mazzuoccolo, Giuseppe; M., Young. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 311:(2011), pp. 32-37. [10.1016/j.disc.2010.09.016]
Graphs of arbitrary excessive class
MAZZUOCCOLO, Giuseppe;
2011
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) showing that all the positive integers can be attained as excessiveclasses of regular graphs.
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