Advertisement

The Edge-Wiener Index and Its Computation for Some Nanostructures

  • Ali Iranmanesh
Chapter
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 7)

Abstract

The first and the second edge versions of Wiener index, which were based on the distance between two edges in a connected graph G, were introduced by Iranmanesh et al. in (MATCH Commun Math Comput Chem 61:663, 2009).

In this chapter, at first we obtain the explicit relation between different versions of Wiener number and due to this relation, the edge-Wiener numbers of some graph have been computed. Then we find the first edge-Wiener index of the composition and sum of graphs. As an application of our results, we find the first and the second edge-Wiener indices of some nanostructures.

Keywords

Connected Graph Topological Index Wiener Index Black Vertex White Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

This work was partially supported by Center of Excellence of Algebraic Hyperstructures and its Applications of Tarbiat Modares University (CEAHA).

References

  1. Azari M, Iranmanesh A (2011) Ars Combinatoria 100:113Google Scholar
  2. Azari M, Iranmanesh A, Tehranian A (2010) Stud Univ Babes bolyai Chemia Liv 4:183Google Scholar
  3. Diudea MV, John PE (2001) MATCH Commun Math Comput Chem 44:103Google Scholar
  4. Gutman I, Potgieter JH (1997) J Serb Chem Soc 62:185Google Scholar
  5. Gutman I, Trinajstic N (1972) Chem Phys Lett 17:535CrossRefGoogle Scholar
  6. Gutman I, Yeh YN, Lee SL, Luo L (1993) Indian J Chem 32A:651Google Scholar
  7. Heydari A, Taeri B (2007a) J Comput Thoer NanoSci 4:158Google Scholar
  8. Heydari A, Taeri B (2007b) MATCH Commun Math Comput Chem 57:665Google Scholar
  9. Iranmanesh A, Kafrani AS (2009) MATCH Commun Math Comput Chem 62:311Google Scholar
  10. Iranmanesh A, Khormali O (2011) J Comput Thoer NanoSci 8:133CrossRefGoogle Scholar
  11. Iranmanesh A, Gutman I, Khormali O, Mahmiani A (2009) MATCH Commun Math Comput Chem 61:663Google Scholar
  12. John PE, Diudea MV (2004) Croat Chem Acta 77:127Google Scholar
  13. Khadikar PV, Karmarkar S (2002) Acta Chim Slov 49:755Google Scholar
  14. Mahmiani A, Khormali O, Iranmanesh A (2010a) Optoelectron Adv Mater Rapid Commun 4:252Google Scholar
  15. Mahmiani A, Khormali O, Iranmanesh A, Ahmadi A (2010b) Optoelectron Adv Mater Rapid Commun 4:256Google Scholar
  16. Nikoli’c S, Trinajsti’c N, Mihali’c Z (1995) Croat Chem Acta 68:105Google Scholar
  17. Sagan BE, Yen YN, Zhang P (1996) Int J Quantum Chem 60:959CrossRefGoogle Scholar
  18. Stevanovic D (2001) Discrete Math 235:237CrossRefGoogle Scholar
  19. Wiener H (1947) J Am Chem Soc 69:17CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsTarbiat Modares UniversityTehranIran

Personalised recommendations