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國立中央大學 2026 · 考試 · 第 35 題

Let matrices A and D represent the Adjacency and Degree matrices of an undirected graph (nn vertices, mm edges) with no self-loops. Let B be an oriented incidence matrix of the same undirected graph. What is the relationship of A, B, and D. (D is the diagonal matrix of vertex degree (n×nn \times n), where the entries di,id_{i,i} is the degree of vertex ii, the number of edges incident to it.)

  • (A)
    B=D−A\mathbf{B} = \mathbf{D} - \mathbf{A}
  • (B)
    BTB=A−D\mathbf{B}^{\mathbf{T}}\mathbf{B} = \mathbf{A} - \mathbf{D}
  • (C)
    BTB=D−A\mathbf{B}^{\mathbf{T}}\mathbf{B} = \mathbf{D} - \mathbf{A}
  • (D)
    BBT=2D−A\mathbf{B}\mathbf{B}^{\mathbf{T}} = 2\mathbf{D} - \mathbf{A}
  • (E)
    BBT=D−A\mathbf{B}\mathbf{B}^{\mathbf{T}} = \mathbf{D} - \mathbf{A}

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