TY - JOUR

T1 - On the core of a unicyclic graph

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Core

KW - König- Egerváry graph

KW - Matching

KW - Maximum independent set

KW - Unicyclic graph

UR - http://www.scopus.com/inward/record.url?scp=84862492737&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.201.6e1

DO - 10.26493/1855-3974.201.6e1

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AN - SCOPUS:84862492737

SN - 1855-3966

VL - 5

SP - 325

EP - 331

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

IS - 2

ER -