Some Distance-Based Topological Indices of a Non-Commuting Graph ABSTRACT | FULL TEXT
Some Distance-Based Topological Indices of a Non-Commuting Graph ABSTRACT | FULL TEXT
___
- Abdollahi, A., Akbari, S. and Maimani, H. R. Non-commuting graph of a group, J. Algebra 298, 468–492, 2006.
- Ashrafi, A. R., Doˇsli´c, T. and Hamzeh, A. The Zagreb coindices of graph operations, Discrete Appl. Math. 158, 1571–1578, 2010.
- Ashrafi, A. R., Doˇsli´c, T. and Saheli, M. The eccentric connectivity index of TUC4C8(R) nanotubes, MATCH Commun. Math. Comput. Chem. 65, 221–230, 2011.
- Ashrafi, A. R., Saheli, M. and Ghorbani, M. The eccentric connectivity index of nanotubes and nanotori, J. Comput. Appl. Math. 235, 4561–4566, 2011.
- Azad, A. and Eliasi, M. Distance in the non-commutative graph of groups, Ars Combinato- ria, in press.
- Buckley, F. and Harary, F. Distances in Graphs (Addison-Wesley, Redwood City, CA, 1990). [7] Darafsheh, M. R. and Poursalavati, N. S. On the existence of the orthogonal basis of the symmetry classes of tensors associated with certain groups, SUT J. Math. 37 (1), 1–17, 2001.
- Ghorbani, M., Ashrafi, A. R. and Hemmasi, M. Eccentric connectivity polynomials of fullerenes, Optoelectron. Adv. Mater. -Rapid Comm. 3 (12), 1306–1308, 2009.
- Gutman, I. Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34, 1087–1089, 1994.
- Gutman, I. and Trinajsti´c, N. Graph theory and molecular orbitals, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, 535–538, 1972.
- Gutman, I. A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes of New York 27, 9–15, 1994.
- Gutman, I. and Das, K. C. The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 83–92, 2004.
- Gutman, I., Yan, W., Yeh, Y. -N. and Yang, B. -Y. Generalized Wiener indices of zigzagging pentachains, J. Math. Chem. 42, 103–117, 2007.
- Isaacs, I. M. Coprime group actions fixing all nonlinear irreducible characters, Canad. J. Math. 41, 68–82, 1989.
- James, G. and Liebeck, M. Representations and Characters of Groups (Second edition, Cambridge Univ. Press, New York, 2001).
- Khalifeh, M. H., Yousefi-Azari, H. and Ashrafi, A. R. The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157, 804–811, 2009.
- Klein, D. J., Lukovits, I. and Gutman, I. On the definition of the hyper-Wiener index for cycle-containing structures, J. Chem. Inf. Comput. Sci. 35, 50-ˆu52, 1995.
- Kumar, V., Sardana, S. and Madan, A. K. Predicting anti-HIV activity of 2,3-diaryl-1,3- thiazolidin-4-ones: computational approaches using reformed eccentric connectivity index, J. Mol. Model. 10, 399-ˆu407, 2004.
- Moghaddamfar, A. R. About noncommuting graphs, Siberian Mathematical Journal 47, 911– 914, 2006.
- Neumann, B. H. A problem of Paul Erd¨os on groups, J. Aust. Math. Soc. Ser. A 21, 467–472, 1976.
- Riedl, J. M. Character degrees, class size, and normal subgroups of a certain class of p- groups, J. Algebra 218 (1), 190–215, 1999.
- Rocke, D. M. p-groups with abelian centralizers, Proc. London Math. Soc. 30 (3), 55–75, 1975.
- Sardana, S. and Madan, A. K. Application of graph theory: Relationship of molecular con- nectivity index, WienerÆs index and eccentric connectivity index with diuretic activity, MATCH Commun. Math. Comput. Chem. 43, 85ˆu-98, 2001.
- Schultz, H. P. Topological organic chemistry 1. Graph theory and topological indices of Alka- nes, J. Chem. Inf. Comput. Sci. 29, 227–228, 1989.
- Sharma, V., Goswami, R. and Madan, A. K. Eccentric connectivity index: A novel highly discriminating topological descriptor for structure-property and structure-activity studies, J. Chem. Inf. Comput. Sci. 37, 273–282, 1997.
- Wiener, H. Structural determination of the paraffin boiling points, J. Am. Chem. Soc. 69, 17–20, 1947.
- West, D. B. Introduction to Graph Theory (Prentice-Hall, Upper Saddle River, NJ, 1996). [28] Zhou, B. Zagreb indices, MATCH Commun. Math. Comput. Chem. 52, 113–118, 2004.
- Zhou, B. and Du, Z. On eccentric connectivity index, MATCH Commun. Math. Com- put. Chem. 63, 181–198, 2010.
- Zhou, B. and Gutman, I. Relations between Wiener, hyper-Wiener and Zagreb indices, Chem. Phys. Lett. 394, 93–95, 2004.
- Zhou, B. and Gutman, I. Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem. 54, 233–239, 2005.