• On the connectivity index for lattices of nonintegral dimensionality

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    • Keywords


      Graph theory; nonintegral dimension; connectivity index

    • Abstract


      We define the connectivity indexc for an infinite graph by the requirement that to disconnect a subset of at leastV points from the rest of the graph requires the deletion of a minimum ofS(V) bonds whereS(V) ∼V(c−1)/c for largeV. For ad-dimensional hypercubical lattice withd integral,c=d. We construct explicit examples of lattices with nonintegral connectivity indexc, 1<c<∞. It is argued that the connectivity index is an important parameter determining the critical behaviour of Hamiltonians on these lattices.

    • Author Affiliations


      Deepak Dhar1

      1. Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400 005, India
    • Dates

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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