Proof of the Strong Conjecture about F-Irregular Graphs in the Class of Graphs \ of Diameter 2

Let F and G be simple finite undirected graphs. A graph G is said to be F -irregular if any two of its distinct vertices belong to different numbers of copies of F in G . According to the strong conjecture about F -irregular graphs (Dovzhenok, Filuta, Chuhai), for any connected graph F of order at least three, there exist infinitely many F -irregular graphs. In this paper, the strong conjecture about F -irregular graphs is confirmed in the class of graphs \ of diameter $$2$$ . It is proved that, for every graph F of diameter $$2$$ , there exists an infinite series of F -irregular graphs of diameter $$3$$ .