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Boundary Condition
Characteristic Polynomial
Free Boundary
Tensor Product
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The energy of a type of lattice
The energy of a type of lattice,10.1016/j.aml.2010.08.034,Applied Mathematics Letters,Luzhen Ye
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The energy of a type of lattice
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Luzhen Ye
The energy of a simple graph G, denoted by E(G), is defined as the sum of the absolute values of eigenvalues of G. Let Gf(m,n) (resp., Gc(m,n) and Gt(m,n)) be the lattice obtained from an m×n square lattice with
free boundary
condition (resp., cylindrical
boundary condition
and the toroidal boundary condition) by adding two diagonal edges to each square. In this work, we obtain the formulae for the energies of Gf(m,n), Gc(m,n), and Gt(m,n). The asymptotic energies of Gf(m,n), Gc(m,n) and Gt(m,n) are also given.
Journal:
Applied Mathematics Letters
, vol. 24, no. 2, pp. 145148, 2011
DOI:
10.1016/j.aml.2010.08.034
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