Independent sets on the Towers of Hanoi graphs
Chen, Hanlin ; Wu, Renfang ; Huang, Guihua ; Deng, Hanyuan
ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016), / Harvested from ARS MATHEMATICA CONTEMPORANEA
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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.

Publié le : 2016-01-01
DOI : https://doi.org/10.26493/1855-3974.783.9b5 
@article{783,
     title = {Independent sets on the Towers of Hanoi graphs},
     journal = {ARS MATHEMATICA CONTEMPORANEA},
     volume = {12},
     year = {2016},
     doi = {10.26493/1855-3974.783.9b5},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/783}
}

Chen, Hanlin; Wu, Renfang; Huang, Guihua; Deng, Hanyuan. Independent sets on the Towers of Hanoi graphs. ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016) . doi : 10.26493/1855-3974.783.9b5. http://gdmltest.u-ga.fr/item/783/