Properties of Sierpinski graphs

A graph is a structure formed by a set of vertices and edges joining pairs of those vertices. There are many types of graphs in the literature and one of them is the Sierpinski graphs. Sierpinski graphs has attracted the attention of many researchers with its interesting properties and has led them to research further on these graphs. In this study, important properties of Sierpinski graphs in literature are compiled. Firstly, the link between Sierpinski graphs and Hanoi graphs are given, and it is also proved that for k ≥ 3, S(n, k) graphs are Hamiltonian graphs. It has been examined whether Sierpinski graphs are planar or not and its various metric features such as eccentricity, diameter, radius, center, and distance between vertices are presented. Lastly, properties related to coloring of Sierpinski graphs are investigated and their properties such as chromatic number, chromatic index, total chromatic number, game color number and game chromatic number are given. Keywords: Graph, Sierpinski graph, Hanoi graph