Constructions of universalized Sierpiński graphs based on labeling manipulations

In this paper, we newly introduce the class of universalized Sierpiński graphs ϒ(G, n) which includes generalized Sierpiński graphs S(n, G) and extended Sierpiński graphs S++(n, k). We then present constructions of universalized Sierpiński graphs based on labeling manipulations which are useful to investigate ϒ(G, n) without depending on the exact n-tuple notation of a vertex in ϒ(G, n). We also present structural properties of universalized Sierpiński graphs such as connectivity, various colorings, hamiltonicity, factorizations, and edge-disjoint factors.