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Counting independent sets in certain classes of (almost) regular graphs

Burstein, Alexander and Kitaev, Sergey and Mansour, Toufik (2008) Counting independent sets in certain classes of (almost) regular graphs. Pure Mathematics and Applications, 19 (2-3). pp. 17-26. ISSN 1218-4586

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Abstract

We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some cases, construct the corresponding bijections.