The generalized S-graphs of diameter 3 Original Research Article

A graph is called a generalized S-graph if for every vertex v of G there exists exactly one vertex v which is more remote from v than every vertex adjacent to v. A generalized S-graph of diameter 3 is called reducible if there is a pair of diametrical vertices v and v such that G—{u, v} v is also a generalized S-graph of diameter 3. Here we determine all irreducible generalized S-graphs of diameter 3.