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

The Number of Maximal Independent Sets in Quasi-Tree Graphs and Quasi-Forest Graphs
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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. 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.
机构地区 Ling Tung University
出处 《Open Journal of Discrete Mathematics》 2017年第3期134-147,共14页 离散数学期刊(英文)
关键词 MAXIMAL Independent Set Quasi-Tree GRAPH Quasi-Forest GRAPH EXTREMAL GRAPH Maximal Independent Set Quasi-Tree Graph Quasi-Forest Graph Extremal Graph
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