Asymptotic incidence energy of lattices

Jia-Bao Liu and Xiang-Feng Pan

Physica A: Statistical Mechanics and its Applications, 2015, vol. 422, issue C, 193-202

Abstract: The energy of a graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. As an analogue to E(G), the incidence energy IE(G), defined as the sum of the singular values of the incidence matrix of G, is a much studied quantity with well known applications in chemical physics. In this paper, based on the results by Yan and Zhang (2009), we propose the incidence energy per vertex problem for lattice systems, and present the closed-form formulae expressing the incidence energy of the hexagonal lattice, triangular lattice, and 33.42 lattice, respectively. Moreover, we show that the incidence energy per vertex of lattices is independent of the toroidal, cylindrical, and free boundary conditions. In particular, the explicit asymptotic values of the incidence energy in these lattices are obtained by utilizing the applications of analysis approach with the help of calculational software.

Keywords: Lattice; Energy; Incidence energy; Laplacian spectrum (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437114010413
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:422:y:2015:i:c:p:193-202

DOI: 10.1016/j.physa.2014.12.006

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().