On the core of a unicyclic graph

Vadim E. Levit, Eugen Mandrescu

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A set S ⊆ V is independent in a graph G = (V, E) if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number α(G) is the cardinality of a maximum independent set, while μ(G) is the size of a maximum matching in G. A connected graph having only one cycle, say C, is a unicyclic graph. In this paper we prove that if G is a unicyclic graph of order n and n - 1 = α(G) + μ(G), then core (G) coincides with the union of cores of all trees in G - C.

Original languageEnglish
Pages (from-to)325-331
Number of pages7
JournalArs Mathematica Contemporanea
Issue number2
StatePublished - 2012


  • Core
  • König- Egerváry graph
  • Matching
  • Maximum independent set
  • Unicyclic graph


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