R-bell Numbers For Graphs

The r-Bell number ^Br(G) of a simple labeled graph G is the number of partitionsrnof its vertex set whose blocks are independent sets of G where the _rst r-verticesrnare in di_erent blocks. The number of these partitions with k blocks is thern(graphical) r- Stirling number ^ Sr(G; k) of G. On this particular paper we willrninvestigate the integer sequence of r-Bell numbers for di_erent kinds of graphs

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