Sierpi\' nski Gasket Graphs and Some of Their Properties

Alberto M. Teguia, Anant P. Godbole

Published 2005-09-12Version 1

The {\it Sierpi\'nski fractal} or {\it Sierpi\'nski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the process that leads to $\Sigma$, and study some of its properties, including its cycle structure, domination number and pebbling number. Various open questions are posed.