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國立中央大學 2026 · 考試 · 第 32 題

The adjacency-matrix representation of a graph G=(V,E)G=(V, E) assumes that the vertices are numbered 1,2,…,∣V∣1, 2, \ldots, |V|. Then the adjacency-matrix representation of a graph GG consists of a ∣V∣×∣V∣|V| \times |V| matrix A=(aij)A = (a_{ij}) such that

aij={1if (i,j)∈E0otherwise.a_{ij} = \begin{cases} 1 & \text{if } (i,j) \in E \\ 0 & \text{otherwise.} \end{cases}

Let V = {1,2,3,4,5} and its adjacency matrix be

12345
101010
200001
300001
401000
500010

Which of the following descriptions is WRONG or the least accurate?

  • (A)
    E={(1,2),(1,4),(2,5),(3,5),(4,2),(5,4)}
  • (B)
    The graph is a directed acyclic graph
  • (C)
    The graph has 5 vertices
  • (D)
    The graph has 6 edges
  • (E)
    There is no path that can go from vertex 1 to vertex 3

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