Fibonacci index and stability number of graphs: a polyhedral study

被引：7
|
作者：
Bruyere, Veronique [1 ]
Melot, Hadrien [1 ]
机构：
[1] Univ Mons, Dept Theoret Comp Sci, B-7000 Mons, Belgium
来源：
JOURNAL OF COMBINATORIAL OPTIMIZATION | 2009年 / 18卷 / 03期
关键词：
Stable set; Fibonacci index; Merrifield-Simmons index; Turan graph; alpha-critical graph; GraPHedron; MERRIFIELD-SIMMONS INDEX; INDEPENDENT SETS; COMBINATORIAL CHEMISTRY; TOPOLOGICAL INDEXES; TURAN GRAPHS; TREES; INEQUALITIES; INVARIANTS; GRAPHEDRON;
D O I：
10.1007/s10878-009-9228-7
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turan graphs frequently appear in extremal graph theory. We show that Turan graphs and a connected variant of them are also extremal for these particular problems. We also make a polyhedral study by establishing all the optimal linear inequalities for the stability number and the Fibonacci index, inside the classes of general and connected graphs of order n.
引用
收藏
页码：207 / 228
页数：22
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