On the intersection of all critical sets of a unicyclic graph

In this paper we prove that if G is a non-König-Egerváry unicyclic graph, then: (i) ker(G)=core(G) and (ii) |corona(G)|+|core(G)|=2α(G)+1. Pay attention that |corona(G)|+|core(G)|=2α(G) holds for every König-Egerváry graph (Levit, 2011) [11].