For general graphs, the computation of all maximal cliques is an NP-hard problem, since it can be reduced to the maximum clique problem which is again a classical NP-complete graph problem [7]. A well-known and popular branch-and-bound based software to compute maximum and maximal cliques in general graphs is Cliquer [8]. Cliquer's runtime is exponential. It will turn out that the maximal clique problem for the graphs considered here is not NP-hard.