Let X be the adjacency matrix of a graph G with no self loops. The entries…
20072007
Let X be the adjacency matrix of a graph G with no self loops. The entries along the principal diagonal of X are
- A.
all zeros
- B.
all ones
- C.
both zeros and ones
- D.
different
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Correct answer: A
In an adjacency matrix, the entry at position (i, j) represents whether there is an edge from vertex i to vertex j. The principal diagonal entries correspond to edges from a vertex to itself (self-loops). Since the graph G has no self-loops, all diagonal entries must be 0.
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