When is G 2 a König-Egerváry Graph?

Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number5
Pages (from-to)1453-1458
Number of pages6
JournalGraphs and Combinatorics
Issue number5
StatePublished - Sep 2013


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


Dive into the research topics of 'When is G 2 a König-Egerváry Graph?'. Together they form a unique fingerprint.

Cite this