Local cutpoints and iterated clique graphs

On the clique behavior of circulants with three small jumps

“…either they are all clique divergent or they are all clique convergent) but this technique does not allow us to determine whether this behavior is convergent or divergent. C n (1, 2, 4) does not have any local cutpoints nor dominated vertices, so the corresponding techniques [8,9] do not work here. Also, C becomes clique convergent when we remove any vertex (K 4 (C −{0}) is already a Helly graph), this implies that C does not have any clique divergent retract (other than itself) hence retractions [20,21] can not be used here.…”