An upper bound on the size of a largest clique in a graph

A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a point‐determining graph is the set G O of all vertices, v , such that G – v is point determining. In this paper we show that the size, ω( G ), of a maximum clique in G satisfies ω( G ) ⩽ 2|π ( G ) O |, where π( G ) (the point determinant of G ) is obtained from G by identifying vertices which have the same neighborhood.