On corona of Konig-Egervary graphs

Let $\alpha (G)$ denote the cardinality of a maximum independent set and $\mu (G)$ be the size of a maximum matching of a graph $G=(V,E)$. If $\alpha (G)+\mu (G)=\mid V\mid$, then $G$ is a König-Egerváry graph, and $G$ is a $1$-König-Egerváry graph whenever $\alpha (G)+\mu (G)=\mid V\mid -1$. The corona $H\circ \mathcal{X}$ of a graph $H$ and a family of graphs $\mathcal{X}=\{X_i:1\le i\le \mid V(H)\mid \}$ is obtained by joining each vertex $v_i$ of $H$ to all the vertices of the corresponding graph $X_i,i=1,2,\mathrm{.}\mathrm{.}\mathrm{.},\mid V(H)\mid$. In this paper we completely characterize graphs whose coronas are $k$-König-Egerváry graphs, where $k\in \{0,1\}$.