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BIRS Workshop Lecture Videos

Distinguishing SierpiÅ ski products of graphs Zemljič, Sara Sabrina


The SierpiÅ ski product of graphs was introduced as a generalization of SierpiÅ ski graphs, which is a fractal-like family of graphs. The main building blocks of SierpiÅ ski graphs are complete graphs and each next iteration is built in the fractal-like manner of a complete graph. This idea was recently generalized to a graph product, where instead of initially taking just one graph, we build a fractal-like structure with two arbitrary graphs, say $G$ and $H$. Intuitively this is done in such a way that the product $G\otimes H$ has $|G|$ copies of graph $H$ which are connected among themselves according to the edges in $G$. So we get a graph with local structure of $H$, but global structure of $G$ (i.e., if we contract all copies of $H$ to a vertex, we get a copy of graph $G$). This construction is interesting because it may yield graphs with distinguishing number greater than 2. In the talk I will describe the SierpiÅ ski products and list some of their basic properties, which may be useful to answer the open question(s) about the distinguishing number of SierpiÅ ski products.

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