Geodesic
The exponential generating functions for sequence of the numbers of $k$-partite graphs
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 84-91

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A specific kind of exponential generating functions for the sequence of the numbers of $k$-partite graphs is considered. These functions take into account the numbers of vertices in each part. A relation is obtained for such generating functions. This relation is a variant of the exponential theorem for these generating functions. It is concluded that it is possible to generalize the obtained relation for hypergraphs and multigraphs. The obtained expression and its simplified special cases are analyzed. The applications of the relations and special cases in physics and mathematics are considered.
Mots-clés : $k$-partite graph
Keywords: hypergraph, multigraph, connected graph, cover, generating functions, exponential theorem. 
@article{PDM_2015_1_a8,
     author = {R. M. Ganopolsky},
     title = {The exponential generating functions for sequence of the numbers of $k$-partite graphs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {84--91},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_1_a8/}
}
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R. M. Ganopolsky. The exponential generating functions for sequence of the numbers of $k$-partite graphs. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 84-91. http://geodesic.mathdoc.fr/item/PDM_2015_1_a8/