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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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