EdgeDelete

EdgeDelete[g, e] makes a graph by deleting the edge e from the graph g.

EdgeDelete[g, {e1, e2, ...}] deletes a collection of edges from g.

EdgeDelete[g, patt] deletes all edges matching the pattern patt.

Examples

Delete a single edge:

EdgeDelete[CompleteGraph[4], 1 <-> 2]

Delete multiple edges:

EdgeDelete[CycleGraph[5], {1 <-> 2, 2 <-> 3}]

Please visit the official Wolfram Language Reference for more details.