A unified approach to the asymptotic topological indices of various lattices

We present a unified approach to the asymptotic topological indices of various lattices.We propose the topological indices per vertex problem for lattice systems.The explicit asymptotic values of Laplacian energies for various lattices are obtained.We deduce the Laplacian energies of many types of lattices are independent of various boundary conditions. In this paper, we present a unified approach to the asymptotic topological indices of various lattices. Moreover, we propose the various topological indices per vertex problem for lattice systems and show that the various topological indices per vertex of lattices are independent of the toroidal, cylindrical, and free boundary conditions. Our result is a generalization of some earlier results.

[1]  The signless Laplacian coefficients and incidence energy of bicyclic graphs , 2013 .

[2]  Yongtang Shi,et al.  Extremal Matching Energy of Bicyclic Graphs , 2013 .

[3]  R. Balakrishnan.  The energy of a graph , 2004 .

[4]  Hong-Hai Li,et al.  Graphs with Extremal Matching Energies and Prescribed Parameters , 2014 .

[5]  Bolian Liu,et al.  A Survey on the Laplacian-Energy-Like Invariant ∗ , 2011 .

[6]  Jinde Cao,et al.  A note on ‘some physical and chemical indices of clique-inserted lattices’ , 2014 .

[7]  D. Cvetkovi.  NEW THEOREMS FOR SIGNLESS LAPLACIAN EIGENVALUES 1 , 2008 .

[8]  Weigen Yan,et al.  Asymptotic energy of lattices , 2008, 0810.0801.

[9]  D. Cvetkovic,et al.  Signless Laplacians of finite graphs , 2007 .

[10]  Weigen Yan,et al.  The triangular kagomé lattices revisited , 2013 .

[11]  Bo Zhou,et al.  On Laplacian Energy , 2013 .

[12]  D. Bozkurt,et al.  On Incidence Energy , 2014 .

[13]  Rao Li,et al.  Lower Bounds for the Kirchhoff Index , 2013 .

[14]  D. Bozkurt,et al.  Sharp Upper Bounds for Energy and Randic Energy , 2013 .

[15]  Dariush Kiani,et al.  On incidence energy of a graph , 2009 .

[16]  F. Y. Wu,et al.  Spanning trees on graphs and lattices in d dimensions , 2000, cond-mat/0004341.

[17]  Bo Zhou,et al.  The Laplacian-energy Like Invariant is an Energy Like Invariant , 2010 .

[18]  Luzhen Ye.  On the Kirchhoff index of some toroidal lattices , 2011 .

[19]  Yongtang Shi,et al.  On a Conjecture about Tricyclic Graphs with Maximal Energy , 2013, 1312.0204.

[20]  Sezer Sorgun.  On Randic Energy of Graphs , 2014 .

[21]  I. Gutman,et al.  On Almost-Equienergetic Graphs , 2013 .

[22]  On Incidence Energy of Trees , 2011 .

[23]  Zuhe Zhang,et al.  Some physical and chemical indices of clique-inserted lattices , 2013, 1302.5932.

[24]  Wasin So,et al.  Graph energy change due to edge deletion , 2008 .

[25]  New Results on the Incidence Energy of Graphs 1 , 2012 .

[26]  Mirjana Lazić,et al.  On the Laplacian energy of a graph , 2006 .

[27]  Jia-Bao Liu,et al.  Asymptotic Laplacian-energy-like invariant of lattices , 2014, Appl. Math. Comput..

[28]  Ante Graovac,et al.  An Upper Bound for Energy of Matrices Associated to an Infinite Class of Fullerenes , 2014 .

[29]  Wasin So,et al.  SINGULAR VALUE INEQUALITY AND GRAPH ENERGY CHANGE , 2007 .

[30]  Jia-Bao Liu,et al.  Asymptotic incidence energy of lattices , 2015 .

[31]  A sharp upper bound on the incidence energy of graphs in terms of connectivity , 2013 .

[32]  I. Gutman,et al.  On Randić energy , 2014 .

[33]  Bolian Liu,et al.  A Laplacian-energy-like invariant of a graph , 2008 .

[34]  Ivan Gutman,et al.  Estimating the Incidence Energy , 2013 .