Answer:
graph 1
Step-by-step explanation:
Let's look at graph 1:
The first vertex (the left hand top corner) has a degree 3 because there are 3 line segments coming from it.
Let's check to see if the other vertices have degree 3.
The second vertex (the middle top) has degree 3 because again it has 3 line segments coming from it.
The third vertex (the top right) has degree 3 because it has 3 line segments coming from it.
The fourth vertex (the bottom left) has degree 3 because it has 3 line segments coming from it.
The fifth vertex (the middle bottom) has degree 3 because it has 3 line segments coming from it.
The last vertex (the bottom right) has degree 3 because it has 3 line segments coming from it.
Let's look at graph 2:
The first vertex (top left) has degree 1 because it has one line segment coming from it.
The second vertex( middle top) has degree 2 because it has 2 line segments coming from it.
Graph 2 doesn't have the same degree per vertex.
Looking at graph 3:
The first vertex (top left) has degree 1 while the second (top middle) has degree 2.
Graph 3 doesn't have the same degree per vertex.
Looking at graph 4:
The top left has degree 1. Looking at one of the middle vertices there, they have degree 4 each because they have 4 line segments coming from it. So graph 4 doesn't have the same degree per vertex.
The answer is only graph 1.
