Geodesic
Independent sets on the Towers of Hanoi graphs
Ars Mathematica Contemporanea, Tome 12 (2017) no. 2, pp. 247-260.

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The number of independent sets is equivalent to the partition function of the hard-core lattice gas model with nearest-neighbor exclusion and unit activity. In this article, we mainly study the number of independent sets i(Hn) on the Tower of Hanoi graph Hn at stage n, and derive the recursion relations for the numbers of independent sets. Upper and lower bounds for the asymptotic growth constant μ on the Towers of Hanoi graphs are derived in terms of the numbers at a certain stage, where μ = limv → ∞(lni(G)) / v(G) and v(G) is the number of vertices in a graph G. Furthermore, we also consider the number of independent sets on the Sierpiński graphs which contain the Towers of Hanoi graphs as a special case.
DOI : 10.26493/1855-3974.783.9b5
Keywords: Independent sets, the Tower of Hanoi graph, Sierpiński graph, recursion relation, asymptotic growth constant, asymptotic enumeration 
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Hanlin Chen; Renfang Wu; Guihua Huang; Hanyuan Deng. Independent sets on the Towers of Hanoi graphs. Ars Mathematica Contemporanea, Tome 12 (2017) no. 2, pp. 247-260. doi : 10.26493/1855-3974.783.9b5. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.783.9b5/

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