Let \(G\) be a simple undirected graph. Denote by \(mi(G)\) the number of maximal independent sets in \(G\). In this paper, we determine the second and third largest number of maximal independent sets in trees. Extremal trees achieving these values are also determined.
Citation
Zemin Jin, Sherry H.F.Yan. Trees with the Second and Third Largest Number of Maximal Independent Sets[J], Ars Combinatoria, Volume 093. 341-351. .