THE SECOND LARGEST NUMBER OF MAXIMAL INDEPENDENT SETS IN GRAPHS WITH AT MOST k CYCLES
THE SECOND LARGEST NUMBER OF MAXIMAL INDEPENDENT SETS IN GRAPHS WITH AT MOST k CYCLES
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DOI：
10.11650/tjm.13.2009.438
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发表时间：
2009-01
影响因子：
0.4
通讯作者：
Zemin Jin;Sherry H. F. Yan
中科院分区：
文献类型：
--
作者：
Zemin Jin;Sherry H. F. Yan
设$G$是一个简单的无向图。用$\mbox{ mi}（G）$（分别为$\mbox{xi}（G）$）表示$G$中最大（分别为最大）独立集的个数。在本文中，我们确定了$\mbox{mi}（G）$的第二大值，最多有$k$圈的图。极值图实现这些值也被确定。
Let $G$ be a simple undirected graph. Denote by $\mbox{ mi}(G)$ (respectively, $\mbox{xi}(G)$) the number of maximal (respectively, maximum) independent sets in $G$. In this paper we determine the second largest value of $\mbox{mi}(G)$ for graphs with at most $k$ cycles. Extremal graphs achieving these values are also determined.