# Corona

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Coronaкорона.

1. The corona $\,coro(G)$ of a graph $\,G$ is a graph obtained from $\,G$ by adding a pendant edge to each vertex of $\,G$. See also Crown of graphs.

2. Let $\,\Omega(G)$ denote the family of all maximum stable sets of the graph $\,G$. We define $\,corona(G) = \cup\{S: \; S \in \Omega(G)\}$ as the set of vertices belonging to some maximum stable sets of $\,G$.

3. $\,G \circ H$ is called the corona of graphs, if it is obtained from the disjoint union of $\,G$ and $\,n$ copies of $\,H$ (where $\,n = |V(G)|$) by joining a vertex $\,x_{i}$ of $\,G$ with every vertex from $\,i$-th copy of $\,H$, for each $\,i = 1, 2, \ldots, n$.

Let $\,k$ be a fixed integer, $\,k \geq 1$, $\,k$-corona $\,kG \circ H$ is a graph obtained from $\,k$ copies of $\,G$ and $\,|V(G)|$ copies of $\,H$ with appropriate edges between each vertex $\,x^{j}_{i}$ of the copy $\,G^{j}$ and all vertices of the copy of $\,H_{i}$.

The $\,2$-corona of a graph $\,H$ is a graph of order $\,3|V(H)|$ obtained from $\,H$ by attaching a path of length $\,2$ to each vertex so that the attached paths are vertex disjoint.

## Литература

• Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.