## Abstract

A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class W_{n} if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W_{1} is the family of all well-covered graphs. Staples showed a number of ways to build graphs in W_{n}, using graphs from W_{n} or W_{n+1}. In this paper, we construct some more infinite subfamilies of the class W_{2} by means of corona, join, and rooted product of graphs.

Original language | English |
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Pages (from-to) | 35-40 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 68 |

DOIs | |

State | Published - Jul 2018 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2018 Elsevier B.V.

## Keywords

- class W
- corona of graphs
- graph join
- independent set
- rooted product of graphs
- shedding vertex
- well-covered graph

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