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