Back
 OJDM  Vol.6 No.2 , April 2016
The Multiplicative Zagreb Indices of Nanostructures and Chains
Abstract: In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube, nanostar and polyomino chain.
Cite this paper: Gao, W. , Farahani, M. and Kanna, M. (2016) The Multiplicative Zagreb Indices of Nanostructures and Chains. Open Journal of Discrete Mathematics, 6, 82-88. doi: 10.4236/ojdm.2016.62008.
References

[1]   Yan, L., Li, Y., Gao, W. and Li, J.S. (2014) On the Extremal Hyper-Wiener Index of Graphs. Journal of Chemical and Pharmaceutical Research, 6, 477-481.

[2]   Yan, L., Li, J.S. and Gao, W. (2014) Vertex PI Index and Szeged Index of Certain Special Molecular Graphs. The Open Biotechnology Journal, 8, 19-22.
http://dx.doi.org/10.2174/1874070701408010019

[3]   Gao, W. and Shi, L. (2014) Wiener Index of Gear fan Graph and Gear Wheel Graph. Asian Journal of Chemistry, 26, 3397-3400.

[4]   Gao, W. and Shi, L. (2015) Szeged Related Indices of Unilateral Polyomino Chain and Unilateral Hexagonal Chain. IAENG International Journal of Applied Mathematics, 45, 138-150.

[5]   Xi, W.F. and Gao, W. (2014) Geometric-Arithmetic Index and Zagreb Indices of Certain Special Molecular Graphs. Journal of Advances in Chemistry, 10, 2254-2261.

[6]   Gao, W. and Wang, W.F. (2014) Second Atom-Bond Connectivity Index of Special Chemical Molecular Structures. Journal of Chemistry, 2014, Article ID: 906254.
http://dx.doi.org/10.1155/2014/906254

[7]   Gao, W. and Wang, W.F. (2015) The Vertex Version of Weighted Wiener Number for Bicyclic Molecular Structures. Computational and Mathematical Methods in Medicine, 2015, Article ID: 418106.
http://dx.doi.org/10.1155/2015/418106

[8]   Gao, W. and Wang, W.F. (2014) Revised Szeged Index and Revised Edge-Szeged Index of Special Chemical Molecular Structures. Journal of Interdisciplinary Mathematics, 4, 417-425.

[9]   Gao, W. and Farahani, M.R. (2016) Degree-Based Indices Computation for Special Chemical Molecular Structures Using Edge Dividing Method. Applied Mathematics and Nonlinear Sciences, 1, 94-117.

[10]   Gao, Y., Gao, W. and Liang, L. (2014) Revised Szeged Index and Revised Edge Szeged Index of Certain Special Molecular Graphs. International Journal of Applied Physics and Mathematics, 4, 417-425.
http://dx.doi.org/10.17706/ijapm.2014.4.6.417-425

[11]   Bondy, J.A. and Mutry, U.S.R. (2008) Graph Theory. Spring, Berlin.
http://dx.doi.org/10.1007/978-1-84628-970-5

[12]   Gutman, I. and Trinajsti, N. (1972) Graph Theory and Molecular Orbitals. III. Total φ-Electron Energy of Alternant Hydrocarbons. Chemical Physics Letters, 17, 535-538.
http://dx.doi.org/10.1016/0009-2614(72)85099-1

[13]   Gutman, I. (2011) Multiplicative Zagreb Indices of Trees. Bulletin of the International Mathematical Virtual Institute, 1, 13-19.

[14]   Ghorbani, M. and Azimi, N. (2012) Note on Multiple Zagreb Indices. Iranian Journal of Mathematical Chemistry, 3, 137-143.

[15]   Eliasi, M., Iranmanesh, A. and Gutman, I. (2012) Multiplicative Versions of First Zagreb Index. MATCH Communications in Mathematical and in Computer Chemistry, 68, 217-230.

[16]   Xu, K. and Das, K.Ch. (2012) Trees, Unicyclic, and Bicyclic Graphs Extremal with Respect to Multiplicative Sum Zagreb Index. MATCH Communications in Mathematical and in Computer Chemistry, 68, 257-272.

[17]   Farahani, M.R. (2014) On Multiple Zagreb Indices of Circumcoronene Homologous Series of Benzenoid. Chemical Physics Research Journal, 7, 277-281.

[18]   Farahani, M.R. (2015) Multiplicative Versions of Zagreb Indices of . Journal of Chemistry and Materials Research, 2, 67-70.

[19]   Shang, Y.L. (2015) Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs. PLoS ONE, 10, E0123426.
http://dx.doi.org/10.1371/journal.pone.0123426

[20]   Shang, Y.L. (2015) The Estrada Index of Evolving Graphs. Applied Mathematics and Computation, 250, 415-423.
http://dx.doi.org/10.1016/j.amc.2014.10.129

 
 
Top