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Counting Water Cells in Bargraphs of Compositions and Set Partitions


Toufik Mansour and Mark Shattuck

Source title: 
Applicable Analysis and Discrete Mathematics, 12(2): 413-438, 2018 (ISI)
Academic year of acceptance: 

If G is a graph and n a positive integer, then the generalized Sierpi´nski graph SnG is a fractal-like graph that uses G as a building block. The construction of SnG generalizes the classical Sierpi´nski graphs Snp , where the role of G is layed 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´nski graphs is also discussed.