Exercise 1.

Which (if any) of the graphs below are the same? Which are different? Explain.

A graph with five vertices; two in a top row, and three in a bottom row. The top-left vertex is adjacent to the top-right vertex, the bottom-right vertex, and the bottom-middle vertex. The top-right vertex is also adjacent to the bottom-middle vertex and the bottom-left vertex. The bottom-middle vertex is adjacent to each of the other bottom vertices.
A graph with five vertices: a row of three, and above the middle vertex of this row, two more vertically aligned. The outer vertices in the row are adjacent to each of the vertices in the middle column. The top and middle vertices in the column are also adjacent.
A graph with five vertices: three are arranged in a top row, and the remaining two are directly below the left and right vertices on the top row. The vertex in the center of the row is adjacent to each of the other vertices. The two vertices on the left are adjacent, as are the two vertices on the right. Finally the top-left and top-right are adjacent by a curved edge.
Solution.
in-context