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We refine an identity between the numbers of certain non-crossing graphs and multigraphs, by modifying a bijection found by P. Podbrdský [A bijective proof of an identity for noncrossing graphs, Discrete Math. 260 (2003) 249–253]. We also prove a new
identity between the number of acyclic non-crossing graphs with n vertices and k edges (isolated vertices allowed and no multiple
edges allowed), and the number of non-crossing connected graphs with n edges and k vertices (multiple edges allowed and no
isolated vertices allowed).
CitacióAlbiol, R.; Noy, M. Identities for non-crossing graphs and multigraphs. "Discrete mathematics", Desembre 2008, vol. 308, núm. 23, p. 5895-5897.