For fragile power domination, two graphs with equal-size sensor sets have identical expected observed-vertex polynomials exactly when their k-subset observation sums agree, and gadget constructions can freely control all but the lowest two coefficients.
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On Fragile Power Domination
For fragile power domination, two graphs with equal-size sensor sets have identical expected observed-vertex polynomials exactly when their k-subset observation sums agree, and gadget constructions can freely control all but the lowest two coefficients.