The Number of Maximal Independent Sets in Quasi-Tree Graphs and Quasi-Forest Graphs

• 作者: Jenq-Jong Lin Min-Jen Jou
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: MAXIMAL Independent Set Quasi-Tree GRAPH Quasi-Forest GRAPH EXTREMAL GRAPH
• 年，卷（期）: 2017,（3）
• 页码范围: 134-147
• 页数: 14页
• 分类号: O1

摘要

A maximal independent set is an independent set that is not a proper subset of any other independent set. A connected graph (respectively, graph) G with vertex set V(G) is called a quasi-tree graph (respectively, quasi-forest graph), if there exists a vertex x ∈V(G) such that G −x?is a tree (respectively, forest). In this paper, we survey on the large numbers of maximal independent sets among all trees, forests, quasi-trees and quasi-forests. In addition, we further look into the problem of determining the third largest number of maximal independent sets among all quasi-trees and quasi-forests. Extremal graphs achieving these values are also given.