Arjana Žitnik: The Sierpinski product of graphs

Povzetek. We introduce a product-like operation that generalizes the construction of the Sierpinski graphs. Some basic properties of the Sierpinski product are presented. In particular, we show that the Sierpinski product of two graphs  is connected if and only if both factors are connected and we present some necessary and sufficient conditions that the factors  must fulfill in order for the product to be planar. As for symmetry properties, we show which automorphisms of factors extend to automorphisms of their Sierpinski product. In many  cases we can also describe the whole automorphism group of the product.