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.
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Levit, V.E., Mandrescu, E. When is G 2 a König–Egerváry Graph?. Graphs and Combinatorics 29, 1453–1458 (2013). https://doi.org/10.1007/s00373-012-1196-5
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DOI: https://doi.org/10.1007/s00373-012-1196-5