Journal of Integer Sequences, Vol. 12 (2009), Article 09.7.1 |

Department of Mathematics

Auburn University

221 Parker Hall

Auburn University, AL 36849

USA

Rhodes Peele

Department of Mathematics

Auburn University Montgomery

P. O. Box 244023

Montgomery, AL 36124-4023

USA

**Abstract:**

The *Bell number* *B*(*G*) of
a simple graph *G* is the number of
partitions of its vertex set whose blocks are independent sets of
*G*. The number of these partitions with *k* blocks is the (graphical)
*Stirling number* *S*(*G*,*k*) of *G*.
We explore integer sequences of
Bell numbers for various one-parameter families of graphs,
generalizations of the relation *B*(*P*_{n})
= *B*(*E*_{n-1})
for path and
edgeless graphs, one-parameter graph families whose Bell number
sequences are quasigeometric, and relations among the polynomial
*A*(*G*,α) = Σ *S*(*G*,*k*)
α^{k},
the chromatic polynomial and the
Tutte polynomial, and some implications of these relations.

(Concerned with sequences A000032 A000045 A000110 A000296 A129847.)

Received April 28 2009;
revised version received October 8 2009.
Published in *Journal of Integer Sequences*, October 13 2009.

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