Generalization of enumeration polynomials for graphs

G\'{a}bor Nyul
Institute of Mathematics, University of Debrecen

Zs\'{o}fia Keresk\'{e}nyi-Balogh
Institute of Mathematics, University of Debrecen

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Minisymposium: COMBINATORICS

Content: B. Duncan and R. Peele were the first who studied enumeration of independent partitions of graphs from a combinatorial point of view, and introduced Stirling numbers of the second kind and Bell numbers for graphs. In our talk, we present properties of these numbers and values for special graphs, as well as their ordered relatives, the so-called Fubini numbers for graphs. In connection with these numbers, we introduce and study some enumeration polynomials for graphs. These results give us an alternative way to investigate several purely combinatorial variants of these numbers and polynomials, for instance, the ordinary, nonconsecutive and $r$-generalized variants.

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