Max-min Rodeg index of bridge graphs and fullerenes
DOI:
https://doi.org/10.11113/mjfas.v14n1.730Keywords:
Topological index, Max-min rodeg index, Fullerenes, Link of two graphs, Bridge graphs.Abstract
Chemical graph theory is a branch of mathematical chemistry which deals with the nontrivial applications of graph theory to solve molecular problems. A graph-based molecular descriptors commonly known as topological indices describe the structures of chemical compounds. They are used in the isomer discrimination, structure property relationship, structure activity relations. Also, the certain physicochemical properties such as boiling point, enthalpy of vaporization, stability, and so on are able to be predicted by this technique. Molecules and molecular compounds are often modeled by molecular graph which is a representation of the structural formula of a chemical compound in terms of graph theory. Recently, the Max-min rodeg index (Mmsde) which is vertex degree-based topological index has attracted attention and gained popularity. This index give the best predictor for enthalpy of vaporization and standard enthalpy of vaporization in the set of octane isomers and also for log water activity coefficient in the set of polychlorobiphenyles. A fullerene graph is a cubic planar graph whose faces are pentagons and hexagons. In this study, the Max-min rodeg index of fullerenes and link of fullerenes is computed. Moreover, it is presented exact expressions for the Max-min rodeg index of bridge graphs.
References
Alizadeh, Y., Andova, V., Klavzar, S., and Škrekovski, R. 2014. Wiener dimension: Fundamental properties and (5, 0)-nanotubical fullerenes. MATCH Communications in Mathematical and in Computer Chemistry, 72, 279-294.
Alizadeh, Y., Iranmanesh, A., and Klavzar, S. 2012. Interpolation Method and Topological Indices: The case of Fullerenes C12k+4. MATCH Communications in Mathematical and in Computer Chemistry, 68, 303-310.
Alizadeh, Y., Iranmanesh, A., andMirzaie, S. 2009. Computing Schultz polynomial, Schultz index of C60 fullerene by gap program. Digest Journal of Nanomaterials and Biostructures, 4(1), 7-10.
Azari, M., Iranmanesh, A., andGutman, I. 2013. Zagreb indices of bridge and chain graphs. MATCH Communications in Mathematical and in Computer Chemistry, 70, 921-938.
De, N. 2017. F-index of bridge and chain graphs. Malaysian Journal of Fundamental and Applied Sciences, 12(3), 109-113.
Ghorbani, M., andHosseinzadeh, M. 2010. On Wiener index of special case of link of fullerenes. Optoelectronics and Advanced Materials-Rapid Communications, 4(4), 538-539.
Ghorbani, M., and Khaksari, A. 2017. On the forgotten topological index. Iranian Journal of Mathematical Chemistry, 8(3), 327-338.
Gutman, I. 1990. A property of the simple topological index. MATCH Communications in Mathematical and in Computer Chemistry, 25, 131-140.
Iranmanesh, A., andZeraatkar, M. 2011. Computing Ga index of HAC5C7 [p, q] and HAC5C6C7 [p, q] nanotubes. Optoelectronics and Advanced Materials− Rapid Communications, 5(7), 790-792.
Kanna, M. R., Kumar, R. P., Jamil, M. K., and Farahani, M. R. 2017. Eccentricity atom-bond connectivity index of polycyclic aromatic hydrocarbon pah^ sub k. International Journal of Pharmaceutical Sciences and Research, 8(1), 201- 206.
Koorepazan-Moftakhar, F., and Ashrafi, A. 2013. Symmetry and PI index of C60+ 12n Fullerenes. Journal of Computational and Theoretical Nanoscience, 10(10), 2484-2486.
Kroto, H. W., Heath, J. R., O'Brien, S. C., Curl, R. F., and Smalley, R. E. 1985. C60: Buckminsterfullerene. Nature, 318(6042), 162-163.
Mansour, T., and Schork, M. 2009a. The PI index of bridge and chain graphs. Match, 61(3), 723.
Mansour, T., and Schork, M. 2009b. The vertex PI index and Szeged index of bridge graphs. Discrete Applied Mathematics, 157(7), 1600-1606.
Mansour, T., and Schork, M. 2010. Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs. Journal of Mathematical Chemistry, 47(1), 72-98.
Nazir, R., Sardar, M. S., Zafar, S., and Zahid, Z. 2017. Edge version of harmonic index and polynomial of some classes of bridge graphs. Bulletin of International Mathematical Virtual Institute, 7(2), 363-371.
Schwerdtfeger, P., Wirz, L. N., andAvery, J. 2015. The topology of fullerenes. Wiley Interdisciplinary Reviews: Computational Molecular Science, 5(1), 96-145.
Shafiei, F. 2015. Relationship between topological indices and thermodynamic properties and of the monocarboxylic acids applications in QSPR. Iranian Journal of Mathematical Chemistry, 6(1), 15-28.
Vukičević, D. 2010. Bond additive modeling 2. Mathematical properties of max-min rodeg index. Croatica Chemica Acta, 83(3), 261-273.
Vukičević, D. 2011. Bond additive modeling 4. QSPR and QSAR studies of the variable adriatic indices. Croatica Chemica Acta, 84(1), 87-91.
Vukičević, D., andGašperov, M. 2010. Bond additive modeling 1. Adriatic indices. Croatica Chemica Acta, 83(3), 243-260.
Wiener, H. 1947. Structural determination of paraffin boiling points. Journal of the American Chemical Society, 69(1), 17-20.
