Which of the following is true for the adjacency matrix of a simple graph?A. Diagonal elements are always zeroB. Diagonal elements are always oneC. All elements are zeroD. All elements are one
Question
Which of the following is true for the adjacency matrix of a simple graph?A. Diagonal elements are always zeroB. Diagonal elements are always oneC. All elements are zeroD. All elements are one
Solution
The correct answer is A. Diagonal elements are always zero.
Here's why:
A simple graph is an undirected graph that has no loops (edges connected at both ends to the same vertex) and no more than one edge between any two different vertices.
In an adjacency matrix of a simple graph, the diagonal elements represent the loops in the graph. Since a simple graph has no loops, the diagonal elements of its adjacency matrix are always zero.
So, option A is correct. Options B, C, and D are incorrect because they do not accurately describe the properties of an adjacency matrix for a simple graph.
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