If all principal diagonal elements of an adjacency matrix are zeros, then the corresponding graph is a **simple graph** that does not have self-loops.

In graph theory, an adjacency matrix is used to represent a graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. Specifically, the entry $ a_{ij} $ in the adjacency matrix is 1 if there is an edge connecting vertex $ i $ and vertex $ j $, and 0 if there is no edge.

When all diagonal entries $ a_{ii} $ are zero, it means there are no edges connecting any vertex to itself, which confirms the absence of self-loops. Therefore, the graph corresponds to a simple graph, which is characterized by:

1. No self-loops: No vertex is connected to itself.
2. No multiple edges: There is at most one edge between any two vertices.

Thus, the final answer is that the corresponding graph is a **simple graph without self-loops**.

Question

If all principal diagonal elements of an adjacency matrix are zeros, then the corresponding graph is a **simple graph** that does not have self-loops.

In graph theory, an adjacency matrix is used to represent a graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. Specifically, the entry $ a_{ij} $ in the adjacency matrix is 1 if there is an edge connecting vertex $ i $ and vertex $ j $, and 0 if there is no edge.

When all diagonal entries $ a_{ii} $ are zero, it means there are no edges connecting any vertex to itself, which confirms the absence of self-loops. Therefore, the graph corresponds to a simple graph, which is characterized by:

1. No self-loops: No vertex is connected to itself.
2. No multiple edges: There is at most one edge between any two vertices.

Thus, the final answer is that the corresponding graph is a **simple graph without self-loops**.

Knowee AI · Accepted Answer

If all principal diagonal elements of an adjacency matrix are zeros, then the corresponding graph is a **simple graph** that does not have self-loops.

In graph theory, an adjacency matrix is used to represent a graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. Specifically, the entry $ a_{ij} $ in the adjacency matrix is 1 if there is an edge connecting vertex $ i $ and vertex $ j $, and 0 if there is no edge.

When all diagonal entries $ a_{ii} $ are zero, it means there are no edges connecting any vertex to itself, which confirms the absence of self-loops. Therefore, the graph corresponds to a simple graph, which is characterized by:

1. No self-loops: No vertex is connected to itself.
2. No multiple edges: There is at most one edge between any two vertices.

Thus, the final answer is that the corresponding graph is a **simple graph without self-loops**.

If all principal diagonal elements of an adjacency matrix are zero’s, then the corresponding graph has

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If all principal diagonal elements of an adjacency matrix are zero’s, then the corresponding graph has

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