gives graph g minus the list of edges edgeList. If g is undirected, then the edges in edgeList are treated as undirected edges; otherwise they are treated as directed edges. If there are multiple edges that qualify, then only one edge is deleted.
DeleteEdges[g, edgeList, All]
will delete all edges that qualify. If only one edge is to be deleted, then edgeList can have the form ; otherwise it has the form .