Department of Mathematics of Xinjiang University, Urumqi, Xinjiang, China
Abstract:
A graph is called a generalized S-graph if for every vertex v of G there exists exactly one vertex
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
such that
v is also a generalized S-graph of diameter 3. Here we determine all irreducible generalized S-graphs of diameter 3.