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

The corresponding graph has no self-loops.

Here's why:

1. An adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.

2. In the adjacency matrix, the entry in the ith row and jth column is typically the number of edges between vertices i and j.

3. The principal diagonal of the adjacency matrix represents the connections from a vertex to itself, i.e., self-loops.

4. If all principal diagonal elements of an adjacency matrix are zero, it means that no vertex has a self-loop. In other words, there are no edges that start and end on the same vertex.