Sierpi\' nski Gasket Graphs and Some of Their Properties

Abstract

The {\it Sierpiński fractal} or {\it Sierpiński 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.

14 pages, 2 Figures

References in corpus (3)

• A Survey of Graph Pebbling
• Conditions for Weighted Cover Pebbling of Graphs
• Cover pebbling numbers and bounds for certain families of graphs

Cited by in corpus (1)

• Graph Hausdorff dimension, Kolmogorov complexity and construction of fractal graphs