Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions.
Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that [Formula: see text], [Formula: see text] and [Formula: see text] have the same asymptotic Laplacian-energy-like invariants.
School of Mathematics and Physics, Anhui Jianzhu University, Hefei, 230601 People's Republic of China.
Jia-Bao
JB
Liu
Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096 People's Republic of China ; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
Jinde
J
Cao
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
Tasawar
T
Hayat
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
Fuad E
FE
Alsaadi
Laplacian spectrum; Laplacian-energy-like invariant; Lattice; Toroidal lattice