4. Let G be an ordered graph, i.e., a pair (V,E) where V is a finit...

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4. Let G be an ordered graph, i.e., a pair (V,E) where V is a finite set of vertices and E C V X V is a set of edges. Let [2(V) and L² (E) denote the vector spaces of complex-valued functions on V and E respectively, endowed with the natural inner product space structure described in class. Let D: L2 (V) [2(E) be the linear transformation defined by = for all (v1,v2) E E. Describe the adjoint D* of D, and compute D* D.

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