Enumeration of labelled digraphs and hypergraphs

We present formulae for the number of labelled k-colored hypergraphs, labelled strongly k-colored hypergraphs, labelled connected hypergraphs, labelled even digraphs and labelled even hypergraphs. We refer to [1] and [2] for the basic definitions. The degree of a vertex v of a hypergraph is the numb...

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Main Authors: Hegde, Malati, Sridharan, M. R.
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description We present formulae for the number of labelled k-colored hypergraphs, labelled strongly k-colored hypergraphs, labelled connected hypergraphs, labelled even digraphs and labelled even hypergraphs. We refer to [1] and [2] for the basic definitions. The degree of a vertex v of a hypergraph is the number of edges Ei of H such that v is in Ei. A hypergraph H is even if every vertex of H has even degree. In an even digraph the sum of indegree and outdegree of every vertex is even. R.C. Read [4] has counted the number of k-colored graphs. Here we generalize this result by extending Read’s method to obtain the formula for the number of labelled k-colored and strongly k-colored hypergraphs.
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title Enumeration of labelled digraphs and hypergraphs
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