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 Enumeration of graphs with given weighted number of connected components Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 1873-1882 https://doi.org/10.4134/BKMS.b150921Published online November 30, 2017 Joungmin Song GIST Abstract : We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of $q$-partite graphs of given order, size and number of connected components. Keywords : $q$-partite graphs, generating functions MSC numbers : 05C30 Downloads: Full-text PDF