Consider the distance between these seven vertices.

1 If 1 of the seven vertices is adjacent to the other two vertices, an isosceles triangle is formed, and the vertices have the same color.

2 If there are no 1 vertices adjacent to two vertices, that is, each vertex is adjacent to 1 vertices at most.

At this time, if A and B are adjacent, then A and B are not adjacent to the vertices except B and A, so adjacent vertices always appear in pairs.

But 7 is an odd number, so there are 1 vertices p that are not adjacent to other vertices.

Consider the distance from p to the other six points.

The distance between two vertices of a regular 13 polygon has six values, but P is not adjacent to the other six points, so the distance is only five values.

So there must be two points with the same distance from p, and these three points form an isosceles triangle with the same vertex color.