The Sierpiński gasket graph of order n is the graph obtained from the connectivity of the Sierpiński sieve. The first few Sierpiński gasket graphs are illustrated above. S_2 is also known as the Hajós graph or the 2-sun graph . Its analog in three dimensions may be termed the Sierpiński tetrahedron graph, and it can be further generalized to higher dimensions (D. Knuth, pers. comm., May 1, 2022). Teguia and Godbole investigated the properties of the Sierpiński gasket graphs and proved that they are Hamiltonian and pancyclic.
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