Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S
is the di erence between maximum and minimum of the distances of the vertex to the vertices
of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set
which is the fair center of some set of vertices is called a fair set. In this paper we prove that the
induced subgraph of any fair set is connected in the case of trees and characterise block graphs
as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The
fair sets of Kn, Km;n, Kne, wheel graphs, odd cycles and symmetric even graphs are identi ed.
The fair sets of the Cartesian product graphs are also discussed