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Open Problems

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The Harary Index of a Graph

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSMATHMETH))

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Abstract

Despite many interesting results on the Harary index and additively or multiplicatively weighted Harary index of graphs reported in the previous chapters, there are still some complicated and challenging problems, which remain open to us, on this topic.

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References

  1. Xu K, Trinajstić N (2011) Hyper-Wiener and Harary indices of graphs with cut edges. Util Math 84:153–163

    MATH  MathSciNet  Google Scholar 

  2. Hendry GRT (1989) On mean distance in certain classes of graphs. Networks 19:451–457

    Article  MATH  MathSciNet  Google Scholar 

  3. Xu K, Liu M, Das KC, Gutman I, Furtula B (2014) A survey on graphs extremal with respect to distance-based topological indices. MATCH Commun Math Comput Chem 71:461–508

    MathSciNet  Google Scholar 

  4. Xu K (2012) Trees with the seven smallest and eight greatest Harary indices. Discret Appl Math 160:321–331

    Article  MATH  Google Scholar 

  5. Das KC, Xu K, Gutman I (2013) On Zagreb and Harary indices. MATCH Commun Math Comput Chem 70:301–314

    MATH  MathSciNet  Google Scholar 

  6. Dankelmann P (1994) Average distance and independence number. Discret Appl Math 51:75–83

    Article  MATH  MathSciNet  Google Scholar 

  7. Gutman I (2002) Relation between hyper-Wiener and Wiener index. Chem Phys Lett 364:352–356

    Article  Google Scholar 

  8. Gutman I, Furtula B (2003) Hyper-Wiener index vs. Wiener index. Two highly correlated structure-descriptors. Monatshefte Math 134:975–981

    Article  Google Scholar 

  9. Zhou B, Gutman I (2004) Relations between Wiener, hyper-Wiener and Zagreb indices. Chem Phys Lett 394:93–95

    Article  Google Scholar 

  10. Alizadeh Y, Iranmanesh A, Došlić T (2013) Additively weighted Harary index of some composite graphs. Discret Math 313:26–34

    Article  MATH  Google Scholar 

  11. Xu K, Wang J, Das KC, Klavžar S (2014) Weighted Harary indices of apex trees and \(k\)-apex trees, manuscript

    Google Scholar 

  12. Lepovic M, Gutman I (1998) A collective property of trees and chemical trees. J Chem Inf Comput Sci 38:823–826

    Article  Google Scholar 

  13. Goldman D, Istrail S, Piccolboni GLA (2000) Algorithmic strategies in combinatorial chemistry. In: Proceedings of the 11th ACM-SIAM symposium on discrete algorithms, pp 275–284

    Google Scholar 

  14. Wang H, Yu G (2006) All but 49 numbers are Wiener indices of trees. Acta Appl Math 92:15–20

    Article  MATH  MathSciNet  Google Scholar 

  15. Li X, Wang L (2003) Solutions for two conjectures on the inverse problem of the Wiener index of peptoids. SIAM J Discret Math 17:210–218

    Article  MATH  Google Scholar 

  16. Li X, Li Z, Wang L (2003) The inverse problems for some topological indices in combinatorial chemistry. J Comput Biol 10:47–55

    Article  Google Scholar 

  17. Xu K, Li J, Zhong L (2012) The Hosoya indices and Merrifield-Simmoms indices of graphs with connectivity at most \(k\). Appl Math Lett 25:476–480

    Article  MATH  MathSciNet  Google Scholar 

  18. Ivanciuc O, Balaban TS, Balaban AT (1993) Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J Math Chem 12:309–318

    Article  MathSciNet  Google Scholar 

  19. Plavšić D, Nikolić S, Trinajstić N, Mihalić Z (1993) On the Harary index for the characterization of chemical graphs. J Math Chem 12:235–250

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

    Kexiang Xu

  2. Department of Mathematics, College of Science, Sungkyunkwan University, Gyeonggi-do, Korea, Republic of Korea

    Kinkar Ch. Das

  3. Rugjer Bošković Institute, Zagreb, Croatia

    Nenad Trinajstić

Authors
  1. Kexiang Xu
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  2. Kinkar Ch. Das
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  3. Nenad Trinajstić
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Corresponding author

Correspondence to Kexiang Xu .

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Xu, K., Das, K.C., Trinajstić, N. (2015). Open Problems. In: The Harary Index of a Graph. SpringerBriefs in Applied Sciences and Technology(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45843-3_6

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