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 excessive classes of regular graphs.
Graphs of arbitrary excessive class
Mazzuoccolo, Giuseppe;
2011-01-01
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 excessive classes of regular graphs.
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