Geodesic
On the number of independent sets in a tree
The electronic journal of combinatorics, Tome 17 (2010)
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We show in a simple way that for any $k,m\in{\Bbb N}$, there exists a tree $T$ such that the number of independent sets of $T$ is congruent to $k$ modulo $m$. This resolves a conjecture of Wagner (Almost all trees have an even number of independent sets, Electron. J. Combin. 16 (2009), # R93).
DOI : 10.37236/467
Classification : 05C69, 05C05 
@article{10_37236_467,
     author = {Hiu-Fai Law},
     title = {On the number of independent sets in a tree},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/467},
     zbl = {1189.05135},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/467/}
}
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Hiu-Fai Law. On the number of independent sets in a tree. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/467

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