We introduce two perturbative spectral descriptors for molecular graphs: the atom-deletion Laplacian response and the bond-deletion Laplacian response. For a hydrogen-suppressed molecular graph these quantities measure the magnitude of the change in Laplacian energy caused by deleting a single atom or a single bond. The construction is deliberately positioned relative to local Laplacian energy: it uses absolute deletion-induced variation to describe sensitivity, whereas signed local quantities retain directional increase or decrease. We cite the corresponding local Laplacian-energy results explicitly and distinguish the elementary estimates used here from sharper estimates already available in the literature. We prove a universal upper bound for the bond-deletion response of an \( n \)-vertex graph and show that it is sharp for every fixed order \( n\geq 2 \); we also record a transparent degree-dependent upper bound for the atom response and give exact benchmark computations for complete graphs and star graphs. On the chemical side, we analyse six representative octane isomer skeletons and then screen the full set of all 18 hydrogen-suppressed octane skeletons. A comparison with Wiener, Randić, Zagreb, and ordinary Laplacian-energy descriptors shows that the new totals \( \mathcal{A} \) and \( \mathcal{B} \), like ordinary Laplacian energy, distinguish all 18 octane skeletons while also providing local deletion-response profiles. A preliminary six-isomer boiling-point test, based on standard NIST values, confirms chemically sensible ordering but does not justify replacing the strongest classical indices on such a small sample. The paper therefore contributes a mathematically explicit sensitivity-descriptor family with preliminary chemical discrimination rather than a completed quantitative structure-property relationship model.