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The Average Eccentricity of Sierpiński Graphs

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Abstract

We determine the eccentricity of an arbitrary vertex, the average eccentricity and its standard deviation for all Sierpiński graphs \({S_p^n}\). Special cases are the graphs \({S_2^{n}}\), which are isomorphic to the state graphs of the Chinese Rings puzzle with n rings and the graphs \({S_3^{n}}\) isomorphic to the Hanoi graphs \({H_3^{n}}\) representing the Tower of Hanoi puzzle with 3 pegs and n discs.

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Authors and Affiliations

  1. FernUniversität in Hagen, 58084, Hagen, Germany

    Andreas M. Hinz

  2. EADS Deutschland GmbH, 81663, Munich, Germany

    Daniele Parisse

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  1. Andreas M. Hinz
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  2. Daniele Parisse
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Correspondence to Andreas M. Hinz.

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Hinz, A.M., Parisse, D. The Average Eccentricity of Sierpiński Graphs. Graphs and Combinatorics 28, 671–686 (2012). https://doi.org/10.1007/s00373-011-1076-4

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  • DOI: https://doi.org/10.1007/s00373-011-1076-4

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