As　a　variant　of　the　Ulam-Kelly＇s　vertex　reconstruction　conjecture　and　the　Harary＇s　edge　reconstruction　conjecture,　Cvetkovie　and　Schwenk　posed　independently　the　following　problem:　can　the　characteristic　polynomial　of　a　simple　graph　G　with　vertex　set　V　be　reconstructed　from　the　characteristic　polynomials　of　all　subgraphs　in　{G　-　v　|　v　is　an　element　of　V}　for　|V|　＞=　3?　This　problem　is　still　open.　A　natural　problem　is:　can　the　characteristic　polynomial　of　a　simple　graph　G　with　edge　set　E　be　reconstructed　from　the　characteristic　polynomials　of　all　subgraphs　in　{G　-　e|e　is　an　element　of　E}?　In　this　paper,　we　prove　that　if　|V|　not　equal　|E|,　then　the　characteristic　polynomial　of　G　can　be　reconstructed　from　the　characteristic　polynomials　of　all　subgraphs　in　{G　-　uv,　G　-　u　-　v|uv　is　an　element　of　E},　and　the　similar　result　holds　for　the　permanental　polynomial　of　G.　We　also　prove　that　the　Laplacian　(resp.　signless　Laplacian)　characteristic　polynomial　of　G　can　be　reconstructed　from　the　Laplacian　(resp.　signless　Laplacian)　characteristic　polynomials　of　all　subgraphs　in　{G　-　e|e　is　an　element　of　E}　(resp.　if　|V|　not　equal　|E|).　(c)　2024　Elsevier　B.V.　All　rights　reserved.