ON THE MAXIMAL INDEPENDENCE POLYNOMIAL OF CERTAIN GRAPH CONFIGURATIONS

被引：0
|
作者：
Hu, Han [1 ,2 ]
Mansour, Toufik [3 ]
Song, Chunwei [1 ,2 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[2] Peking Univ, LMAM, Beijing 100871, Peoples R China
[3] Univ Haifa, Dept Math, IL-31905 Haifa, Israel
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2017年 / 47卷 / 07期
关键词：
Maximal independence; recurrence; unimodality; Chebyshev polynomial; bridge path; bridge cycle; STABLE SETS; BIPARTITE GRAPHS; NUMBER; ROOTS; UNIMODALITY; VERTICES;
D O I：
10.1216/RMJ-2017-47-7-2219
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate the maximal independence polynomials of some popular graph configurations. Through careful analysis, some of the polynomials under study are shown to be Chebyshev, which helps characterize polynomial properties such as unimodality, log-concavity and real-rootedness with ease and efficiency. We partially characterize the bridge path and bridge cycle graphs of wheels and fans according to their unimodality properties and propose relevant open problems. Also, to compare with the usual independence polynomials, we provide analogous results regarding the vertebrated graph, and the firecracker graph, as studied by Wang and Zhu [47].
引用
收藏
页码：2219 / 2253
页数：35
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