True or False: The adjacency matrix for any graph with 5 edges has 5 rows and 5 columns.
Question
True or False: The adjacency matrix for any graph with 5 edges has 5 rows and 5 columns.
Solution
False. The adjacency matrix for a graph is determined by the number of vertices, not edges. The adjacency matrix is a square matrix where the number of rows and columns is equal to the number of vertices in the graph. So, a graph with 5 edges could have any number of vertices, and therefore any size adjacency matrix, depending on its structure.
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