Counting Water Cells in Bargraphs of Compositions and Set Partitions
Counting Water Cells in Bargraphs of Compositions and Set Partitions
Source title:
Applicable Analysis and Discrete Mathematics, 12(2): 413-438,
2018
(ISI)
Academic year of acceptance:
2018-2019
Abstract:
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.