On corona of Konig-Egervary graphs

Abstract

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=\left( V,E\right) $. If $α(G)+μ(G)=\left\vert V\right\vert $, then $G$ is a König-Egerváry graph, and $G$ is a $1$-König-Egerváry graph whenever $α(G)+μ(G)=\left\vert V\right\vert -1$. The corona $H\circ\mathcal{X}$ of a graph $H$ and a family of graphs $\mathcal{X}=\left\{ X_{i}:1\leq i\leq\left\vert V(H)\right\vert \right\} $ is obtained by joining each vertex $v_{i}$ of $H$ to all the vertices of the corresponding graph $X_{i},i=1,2,...,\left\vert V(H)\right\vert $. In this paper we completely characterize graphs whose coronas are $k$-König-Egerváry graphs, where $k\in\left\{ 0,1\right\} $.