According to Kirchhoff's theorem, the cofactors of a matrix representation of this operator count the number of spanning trees. (15[2])In algebraic (15[1])graph theory, (-5[1])the discrete form of this operator is the difference between the degree (15[1])and adjacency matrices. (15[3])Elliptic (15[1])operators generalize this operator, (-5[2])whose kernel consists of functions that satisfy (15[1])the maximum principle, meaning (15[2])they attain extrema on their boundary. A (15[1])function f is harmonic if this operator (15[1])of f equals zero; (15[3])that (15[1])(*) PDE (10[2])is named after this operator’s (-5[1])namesake and is (10[1])the homogeneous version of Poisson’s (10[1])equation. (10[3])The divergence of the gradient (10[1])gives this operator, (10[2])which is (10[1])symbolized with a triangle or as del-squared. (10[3])For (10[1])10 points, give this differential operator (10[2])named for a French (10[1]-5[1])mathematician (10[2])who also has a namesake real-to-complex transform. ■END■ (10[3]0[4])