The Kirchhoff Index of Toroidal Meshes and Variant Networks
Joint Authors
Pan, Xiang-Feng
Liu, Jia-Bao
Cao, Jinde
Huang, Xia
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-03
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The resistance distance is a novel distance function on electrical network theory proposed by Klein and Randić.
The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices in G.
In this paper, we established the relationships between the toroidal meshes network Tm×n and its variant networks in terms of the Kirchhoff index via spectral graph theory.
Moreover, the explicit formulae for the Kirchhoff indexes of L(Tm×n), S(Tm×n), T(Tm×n), and C(Tm×n) were proposed, respectively.
Finally, the asymptotic behavior of Kirchhoff indexes in those networks is obtained by utilizing the applications of analysis approach.
American Psychological Association (APA)
Liu, Jia-Bao& Pan, Xiang-Feng& Cao, Jinde& Huang, Xia. 2014. The Kirchhoff Index of Toroidal Meshes and Variant Networks. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-460509
Modern Language Association (MLA)
Liu, Jia-Bao…[et al.]. The Kirchhoff Index of Toroidal Meshes and Variant Networks. Mathematical Problems in Engineering No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-460509
American Medical Association (AMA)
Liu, Jia-Bao& Pan, Xiang-Feng& Cao, Jinde& Huang, Xia. The Kirchhoff Index of Toroidal Meshes and Variant Networks. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-460509
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460509