Nonisomorphic graphs may have the same domination polynomial. Such graphs are said to be dominating equivalent, dominating nonunique, or co-dominating graphs.
The numbers of dominating nonunique graphs on 
, 2, ... vertices are 0, 0, 0, 2, 13, 104, 876, 11680, 271063,
11977655, ... (OEIS A378517). The 15 Dominating
nonunique graphs on five or fewer vertices are illustrated above.
A graph that does not share a domination polynomial with any other nonisomorphic graph is said to be a dominating unique graph (Akbari et al. 2010).
