On the Core of a Unicyclic Graph

Details On the Core of a Unicyclic Graph On the Core of a Unicyclic Graph

2011-02-23

arxiv.org/abs/1102.4727v1

Computer Science

Discrete Mathematics

8 pages, 5 figures

Scientific paper

A set S is independent in a graph G if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(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 = alpha(G) + mu(G), then core(G) coincides with the union of cores of all trees in G-C.

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