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Graphs and Combinatorics

, Volume 28, Issue 5, pp 671–686 | Cite as

The Average Eccentricity of Sierpiński Graphs

  • Andreas M. HinzEmail author
  • Daniele Parisse
Original Paper

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.

Keywords

Sierpiński graphs Eccentricity Average eccentricity Tower of Hanoi Hanoi graphs Integer sequences 

Mathematics Subject Classification (2010)

05C12 05A10 11B83 11B73 

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Copyright information

© Springer 2011

Authors and Affiliations

  1. 1.FernUniversität in HagenHagenGermany
  2. 2.EADS Deutschland GmbHMunichGermany

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