Journal of Mathematical Chemistry

, Volume 46, Issue 4, pp 1377–1393 | Cite as

Bounds on Harary index

  • Kinkar Ch. DasEmail author
  • Bo Zhou
  • N. Trinajstić
Original Paper


In this paper, we obtain the lower and upper bounds on the Harary index of a connected graph (molecular graph), and, in particular, of a triangle- and quadrangle-free graphs in terms of the number of vertices, the number of edges and the diameter. We give the Nordhaus–Gaddum-type result for Harary index using the diameters of the graph and its complement. Moreover, we compare Harary index and reciprocal complementary Wiener number for graphs.


Harary index Triangle-free graphs Quadrangle-free graphs Diameter Lower bound Upper bound 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonRepublic of Korea
  2. 2.Department of MathematicsSouth China Normal UniversityGuangzhouPeople’s Republic of China
  3. 3.The Rugjer Bošković InstituteZagrebCroatia

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