As　a　variant　of　the　Ulam-Kelly＇s　vertex　reconstruction　conjecture　and　the　Harary＇s　edge　reconstruction　conjecture,　Cvetković　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∈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∈E}?　In　this　paper,　we　prove　that　if　|V|≠|E|,　then　the　characteristic　polynomial　of　G　can　be　reconstructed　from　the　characteristic　polynomials　of　all　subgraphs　in　{G−uv,G−u−v|uv∈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∈E}　(resp.　if　|V|≠|E|).　©　2024　Elsevier　B.V.