## Abstract

The independence number of a graph G, denoted by α(G), is the cardinality of a maximum independent set, and μ(G) is the size of a maximum matching in G. If α(G) + μ(G) equals its order, then G is a König-Egerváry graph. The square of a graph G is the graph G ^{2} with the same vertex set as in G, and an edge of G ^{2} is joining two distinct vertices, whenever the distance between them in G is at most two. G is a square-stable graph if it enjoys the property α(G) = α(G ^{2}). In this paper we show that G ^{2} is a König-Egerváry graph if and only if G is a square-stable König-Egerváry graph.

Original language | English |
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Pages (from-to) | 1453-1458 |

Number of pages | 6 |

Journal | Graphs and Combinatorics |

Volume | 29 |

Issue number | 5 |

DOIs | |

State | Published - Sep 2013 |

Externally published | Yes |

## Keywords

- Maximum independent set
- Perfect matching
- Square of a graph

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