Independent sets on the Towers of Hanoi graphs - Chen, Hanlin (Ars mathematica contemporanea, 2017)
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 ?$i(H_n)$? on the Tower of Hanoi graph ?$H_n$? 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 ?$μ = \lim_{v → ∞} \frac{\ln i(G)}{v(G)}$? 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.
Keywords: asimptotsko preštevanje; graf Sierpińskega; grafi Hanojskih stolpov; konstanta asimptotske rasti; neodvisne množice; rekurzivna zveza