Here's a non-regular one:
Graph 1, order 9.
0 : 3 6 7;
1 : 4 6 8;
2 : 5 7 8;
3 : 0 6 7;
4 : 1 6 8;
5 : 2 7 8;
6 : 0 1 3 4;
7 : 0 2 3 5;
8 : 1 2 4 5;
Now the list of pairwise distances
0 2 2 1 2 2 1 1 3
2 0 2 2 1 2 1 3 1
2 2 0 2 2 1 3 1 1
1 2 2 0 2 2 1 1 3
2 1 2 2 0 2 1 3 1
2 2 1 2 2 0 3 1 1
1 1 3 1 1 3 0 2 2
1 3 1 1 3 1 2 0 2
3 1 1 3 1 1 2 2 0