The triangular kagomé lattices revisited

• DOI: 10.1016/j.physa.2013.07.030
• Publication Date: 2013-07-31T07:16:23Z
• Authors: Xiaoyun Liu; Weigen Yan
• Keywords: 0103 physical sciences; 01 natural sciences

Abstract The dimer problem, Ising spins and bond percolation on the triangular kagome lattice have been studied extensively by physicists. In this paper, based on the fact the triangular kagome lattice with toroidal boundary condition can be regarded as the line graph of 3.12.12 lattice with toroidal boundary condition, we derive the formulae of the number of spanning trees, the energy, and the Kirchhoff index of the triangular kagome lattice with toroidal boundary condition.