  A set S is independent in a graph G if no two vertices from S are adjacent.
The independence number alpha(G) is the cardinality of a maximum independent
set, while mu(G) is the size of a maximum matching in G. If alpha(G)+mu(G)=|V|,
then G=(V,E) is called a Konig-Egervary graph. The number
d_{c}(G)=max{|A|-|N(A)|} is called the critical difference of G (Zhang, 1990).
By core(G) (corona(G)) we denote the intersection (union, respectively) of all
maximum independent sets, while by ker(G) we mean the intersection of all
critical independent sets. A connected graph having only one cycle is called
unicyclic. It is known that ker(G) is a subset of core(G) for every graph G,
while the equality is true for bipartite graphs (Levit and Mandrescu, 2011).
For Konig-Egervary unicyclic graphs, the difference |core(G)|-|ker(G)| may
equal any non-negative integer. In this paper we prove that if G is a
non-Konig-Egervary unicyclic graph, then: (i) ker(G)= core(G) and (ii)
|corona(G)|+|core(G)|=2*alpha(G)+1. Pay attention that
|corona(G)|+|core(G)|=2*alpha(G) holds for every Konig-Egervary graph.
