2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104897We present some Pfaffian identities, which are completely different from the Plücker relations. As consequences we obtain a quadratic identity for the number of perfect matchings of plane graphs, which has a simpler form than the formula by Yan et al (Graphical condensation of plane graphs: a combinatorial approach, Theoret. Comput. Sci., to appear), and we also obtain some new determinant identities.22 pages, 2 figuresCombinatorics05C70; 05C90text