On König–Egerváry corona graphs

Let α(G) denote the cardinality of a maximum independent set and μ(G) be the size of a maximum matching of a graph G=VG,EG. If α(G)+μ(G)=VG-k, then G is a k -König–Egerváry graph. In particular, if k=0, then G is a König–Egerváry graph. The coronaH∘X of a graph H and a family of graphs X=Xi:1≤i≤V(H) is obtained by joining each vertex vi of H to all the vertices of the corresponding graph Xi,i=1,2,..,V(H). In this paper we completely characterize graphs whose coronas are k-König–Egerváry graphs, where k∈0,1.