  Given a non empty set $S$ of vertices of a graph, the partiality of a vertex
with respect to $S$ is the difference 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 $K_{n}$,
$K_{m,n}$, $K_{n}-e$, wheel graphs, odd cycles and symmetric even graphs are
identified. The fair sets of the Cartesian product graphs are also discussed.
