Some Topological Indices of Edge Corona of Two Graphs

Document Type: Research Paper

Authors

1 University of Mysore, India

2 PES University, India

10.22052/ijmc.2017.34313.1132

Abstract

In this paper, we compute the Wiener index, first Zagreb index, second
Zagreb index, degree distance index and Gutman index of edge corona of
two graphs. Also in some cases we derive formulas for Weiner index, Zagreb indices, degree distance and Gutman index in terms of vertices and edges .

Keywords

Main Subjects


 

  1. A. R. Ashrafi, M. Ghorbani, M. Jalali, The vertex PI and Szeged indices of an infinite family of fullerenes, J. Theor. Comput. Chem.7 (2008) 221–231.
  2. V. Andova, D. Dimitrov, J. Fink, R. Skrekovski, Bounds on Gutman index, MATCH Commun. Math. Comput. Chem.67 (2012) 515–524.
  3. P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, On the degree distance of a graph, Discrete Appl. Math. 157 (2009) 2773–2777.
  4. P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, The edge-Wiener index of a graph, Discrete Math. 309 (2009) 3452–3457.
  5. A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta. Appl. Math. 66 (2001) 211–249.
  6. A. A. Dobrynin, I. Gutman, S. Klav ar, P. igert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002) 247–294.
  7. A. A. Dobrynin, A. A. Kochetova, Degree distance of a graph: a degree analogue of the Wiener index, J. Chem. Inf. Comput.Sci. 34 (1994) 1082–1086.
  8. M. Essalih, M. E. Marraki and G. E. Hagri, Calculation of some topological indices of graphs, J. Theor. Appl. Inf. Tech. 30 (2011) 122–127.
  9. R. Frucht, F. Harary, On the corona of two graphs, Aequationes Math. 4 (1970) 322–325.
  10. L. Feng, W. Liu, The maximal Gutman index of bicyclic graphs, MATCH Commun. Math. Comput. Chem. 66 (2011) 699–708.
  11. I. Gutman, Selected properties of Schultz molecular topological index, J. Chem. Inf. Coumput. Sci. 34 (1994) 1087–1089.
  12. I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes New York 27 (1994) 9–15.
  13. I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86 (2013) 351–361.
  14. I. Gutman, K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83–92.
  15. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals, Total  electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
  16. I. Gutman, S. Klav ar, B. Mohar (eds.), Fifty years of the Wiener index, MATCH Commun. Math. Comput. Chem. 35 (1997) 1–259.
  17. Y. Hou, W.-C. Shiu, The spectrum of the edge corona of two graphs, Electron. J. Linear Algebra 20 (2010) 586–594.
  18. A. Iranmanesh, I. Gutman, O. Khormali, A. Mahmiani, The edge versions of Wiener index, MATCH Commun. Math. Comput. Chem. 61 (2009) 663–672.
  19. M. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009) 804–811.
  20. M. Liu, B. Liu, A survey on recent results of variable Wiener index, MATCH Commun. Math. Comput. Chem. 69 (2013) 491–520.
  21. M. Knor, P. Potocnik, R. Skrekovski, Relationship between the edge-Wiener indexand the Gutman index of a graph, Discrete Appl. Math. 167 (2014) 197–201.
  22. B. E. Sagan, Y. N. Yeh, P. Zhang, The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (1996) 959–969.
  23. V. S. Agnes, Degree distance and Gutman index of corona product of graphs, Trans. Comb. 4 (3) (2015) 11–23.
  24. I. Tomescu, Some extremal properties of the degree distance of a graph, Discrete Appl. Math. 98 (1999) 159–163.
  25. A. I. Tomescu, Unicyclic and bicyclic graphs having minimum degree distance, Discrete Appl. Math. 156 (2008) 125–130.
  26. H. Wiener, Structrual determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.
  27. Z. Yarahmadi, A. R. Ashrafi, The Szeged, vertex PI, first and second Zagreb indices of corona product of graphs, Filomat 26 (3) (2012) 467–472.