, Volume 15, Issue 6, pp 545–549 | Cite as

On the connectivity index for lattices of nonintegral dimensionality

  • Deepak Dhar
Statistical Mechanics


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.


Graph theory nonintegral dimension connectivity index 


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Copyright information

© Indian Academy of Sciences 1980

Authors and Affiliations

  • Deepak Dhar
    • 1
  1. 1.Tata Institute of Fundamental ResearchBombayIndia

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