On graphs with maximal independent sets of few sizes, minimum degree at least 2, and girth at least 7.

Abstract: We prove that for integers and with and , there are only finitely many connected graphs of minimum degree at least 2, maximum degree at most , and girth at least 7 that have maximal independent sets of at most different sizes. Furthermore, we prove several results restricting the degrees of such graphs. Our contributions generalize known results on well-covered graphs. [Copyright &y& Elsevier]