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“School of Mathematics”

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Paper   IPM / M / 11342
School of Mathematics
  Title:   Wiener-type invariants of some graph operations
  Author(s):  A. R. Ashrafi (Joint with S. Hossein-Zadeh and A. Hamzeh)
  Status:   Published
  Journal: Filomat
  Vol.:  23
  Year:  2009
  Pages:   103-113
  Supported by:  IPM
  Abstract:
Let d(G, k) be the number of pairs of vertices of a graph G that are at distance k, λ a real number, and Wλ(G)=∑k ≥ 1d(G,k)kλ is called the Wiener-type invariant of G associated to real number λ. In this paper, the Wiener-type invariants of some graph operations are computed. As immediate consequences, the formulae for reciprocal Wiener index, Harary index, hyper- Wiener index and Tratch-Stankevich-Zefirov index are calculated. Some upper and lower bounds are also presented.

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