Connectivity and some other properties of generalized Sierpiński graphs
Sandi Klavzar, Sara Zemljic
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Source: Crossref
Published: Jan 1, 2018
DOI: 10.2298/aadm170206009k
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If G is a graph and n a positive integer, then the generalized Sierpi?ski graph SnG is a fractal-like graph that uses G as a building block. The construction of SnG generalizes the classical Sierpi?ski graphs Sn p, where the role of G is played by the complete graph Kp. An explicit formula for the number of connected components in SnG is given and it is proved that the (edge-)connectivity of SnG equals the (edge-)connectivity of G. It is demonstrated that SnG contains a 1-factor if and only if G contains a 1-factor. Hamiltonicity of generalized Sierpi?ski graphs is also discussed.
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