[Translate to English:] Seminár z teórie grafov - Sara Zemljic (14.12.2017)
Thursday 14.12.2017 at 9:50, Lecture room M/213
Sara Zemljic:
The Sierpinski product of graphs
Abstrakt:
The family of Sierpinski graphs has been studied very often in the past few decades for different reasons. One of them is definitely their relation to the famous Sierpinski tringle fractal and their fractal-like structure. Main building block of Sierpinski 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 generalized Sierpinski graphs, where instead of initially taking a complete graph, we start with an arbitrary graph G. Next iterations are then build in the same manner as graph G is constructed.
We have generalized this idea even further by defining a Sierpinski product of two arbitrary graphs G and H, where we take |G| copies of a graph H and connect these according to edges in graph G. So intuitively we get a graph with local structure of H, but global structure of G. That is if we contract all copies of H, we get a copy of graph G.
In the talk I will describe the Sierpinski product and related constructions, and list some of their basic properties and examples.