I am not a mathematician so please take that into consideration when formulating your answers.
Technically 2 graphs are NOT isomorphic if any one of the countless graph invariants (i.e. vertices, edges, etc…) are not the same for both graphs.
I would like to know in this case which graph invariant is different between Graph A and Graph B for this covering design (v=10, k=6, t=3) which proves that Graph A and Graph B are NOT isomorphic. Furthermore, how is it calculated?
Graph A
1, 2, 3, 4, 6, 7
1, 2, 3, 5, 7, 10
1, 2, 3, 8, 9, 10
1, 2, 4, 6, 8, 10
1, 3, 4, 5, 6, 9
1, 4, 5, 7, 8, 9
2, 4, 5, 6, 9, 10
2, 5, 6, 7, 8, 9
3, 4, 5, 7, 8, 10
3, 6, 7, 8, 9, 10
Graph B
1, 2, 3, 4, 6, 7
1, 2, 3, 5, 8, 10
1, 2, 3, 7, 9, 10
1, 2, 4, 6, 8, 10
1, 3, 4, 5, 6, 9
1, 4, 5, 7, 8, 9
2, 4, 5, 6, 9, 10
2, 5, 6, 7, 8, 9
3, 4, 5, 7, 8, 10
3, 6, 7, 8, 9, 10
The only difference between Graph A and Graph B is in blocks 2 & 3 where the 7 and the 8 are inverted. All the other blocks are the same.
Thanks Roy