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Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT 

Year 2012, Volume: 41 Issue: 4, 515 - 526, 01.04.2012

References

  • 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.

Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT 

Year 2012, Volume: 41 Issue: 4, 515 - 526, 01.04.2012

References

  • 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.
There are 29 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

M. Mirzargar This is me

 a.r. Ashrafi This is me

Publication Date April 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 4

Cite

APA Mirzargar, M., & Ashrafi, . (2012). Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics, 41(4), 515-526.
AMA Mirzargar M, Ashrafi . Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. April 2012;41(4):515-526.
Chicago Mirzargar, M., and  a.r. Ashrafi. “Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 41, no. 4 (April 2012): 515-26.
EndNote Mirzargar M, Ashrafi  (April 1, 2012) Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics 41 4 515–526.
IEEE M. Mirzargar and  . Ashrafi, “Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT ”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 4, pp. 515–526, 2012.
ISNAD Mirzargar, M. - Ashrafi, a.r. “Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 41/4 (April 2012), 515-526.
JAMA Mirzargar M, Ashrafi . Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2012;41:515–526.
MLA Mirzargar, M. and  a.r. Ashrafi. “Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 4, 2012, pp. 515-26.
Vancouver Mirzargar M, Ashrafi . Some Distance-Based Topological Indices of a Non-Commuting Graph  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2012;41(4):515-26.