关于单圈图的核
On the Core of a Unicyclic Graph
摘要：
一个集合S在图G中是独立的，如果S中没有两个顶点是相邻的。核心（G）是指所有最大独立集的交集。独立数alpha（G）是最大独立集的基数，而mu（G）是G中最大匹配的大小。一个只有一个圈的连通图，比如C，是单圈图。本文证明了：若G是n阶单圈图，且n-1 = alpha（G）+ mu（G），则核（G）与G-C中所有树的核的并重合.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
