If the incidence matrix of a graph has five identical columns, then the graph G has

The graph G has five identical vertices.

Here's why:

The incidence matrix of a graph is a matrix that represents the relationship between vertices and edges of the graph. Each row of the matrix represents an edge, and each column represents a vertex.

If a column is identical to another, it means that the corresponding vertex has the same connections as the other vertex. In other words, they have the same edges.

Therefore, if the incidence matrix of a graph has five identical columns, it means that there are five vertices in the graph that have the same connections. These vertices are identical in terms of their connections to other vertices.