Test case generation from context-free grammars typically uses the grammar's production rules to directly construct words that cover specific sets of derivations. Here, we investigate test case generation by traversing graphs derived from the LR-automata corresponding to the grammars. We develop a new algorithm that generates positive test cases by covering all edges between pairs of directly connected states in a two-phase breadth-first path search. The algorithm iterates over all edges stemming from shift/reduce and reduce/reduce conflicts, using a technique similar to the stack duplication used in GLR parsing. We then extend our algorithm to generate negative (i.e., syntactically invalid) test cases, by applying different edge mutation operations during the extraction of test cases from paths.