Sierpi\' nski Gasket Graphs and Some of Their Properties

Details Sierpi\' nski Gasket Graphs and Some of Their Properties Sierpi\' nski Gasket Graphs and Some of Their Properties

2005-09-12

arxiv.org/abs/math/0509259v1

Australasian Journal of Combinatorics, 35, 181--192, 2006

Mathematics

Combinatorics

14 pages, 2 Figures

Scientific paper

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.

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