Study of dimer–monomer on the generalized Hanoi graph

Wei Bang Li, Shu Chiuan Chang

Research output: Contribution to journalArticlepeer-review


We study the number of dimer–monomers Md(n) on the Hanoi graphs Hd(n) at stage n with dimension d equal to 3 and 4. The entropy per site is defined as zHd=limv→∞lnMd(n)/v, where v is the number of vertices on Hd(n). We obtain the lower and upper bounds of the entropy per site, and the convergence of these bounds approaches to zero rapidly when the calculated stage increases. The numerical values of zHd for d= 3 , 4 are evaluated to more than a hundred digits correct. Using the results with d less than or equal to 4, we predict the general form of the lower and upper bounds for zHd with arbitrary d.

Original languageEnglish
Article number77
JournalComputational and Applied Mathematics
Issue number2
Publication statusPublished - 2020 May 1

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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