2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132028Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.22 pagesGeometric TopologyCombinatorics57M25;05C10text