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.