Extremal Multi-bridge Graphs With Respect To Merrifield-Simmons Index

被引：0

作者：

Chen, Shubo ^{[2
]}

Liu, Weijun ^{[1
]}

机构：

[1] Nantong Univ, Sch Sci, Nantong 226007, Jiangsu, Peoples R China

[2] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China

来源：

ARS COMBINATORIA | 2011年 / 102卷

关键词：

HEXAGONAL CHAINS; UNICYCLIC GRAPHS; HOSOYA INDEXES; FIBONACCI NUMBERS; INDEPENDENT SETS; ENUMERATION; SUBSETS; TREES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Merrifield-Simmons index of a graph G, denoted by i(G), is defined to be the total number of its independent sets, including the empty set. Let theta(a(1), a(2), ..., a(k)) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a(1), a(2), ..., a(k) respectively, we named it as multi-bridge graphs for convenience. Tight upper and lower bounds for the Merrifield-Simmons index of theta(a(1), a(2), ..., a(k)) are established in this paper.

引用

页码：161 / 172

页数：12

共 50 条

[31] The Merrifield-Simmons index of some lexicographic product graphs
Tian, Shuangliang
Chen, Meijun
Chen, Ping
He, Xue
2016 8TH INTERNATIONAL CONFERENCE ON INTELLIGENT HUMAN-MACHINE SYSTEMS AND CYBERNETICS (IHMSC), VOL. 2, 2016, : 13 - 16
[32] Orderings of a class of trees with respect to the Merrifield-Simmons index and the Hosoya index
Tian, Wenwen
Zhao, Fei
Sun, Zheng
Mei, Xuesong
Chen, Guangde
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2019, 38 (04) : 1286 - 1295
[33] On computing Merrifield-Simmons index
Ahmadi, M. B.
Seif, Z.
OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS, 2010, 4 (01): : 56 - 58
[34] On the Merrifield-Simmons index of trees
Li, XL
Zhao, HX
Gutman, I
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2005, 54 (02) : 389 - 402
[35] The Hosoya index and the Merrifield-Simmons index
Huang, Yufeng
Shi, Lingsheng
Xu, Xingyu
JOURNAL OF MATHEMATICAL CHEMISTRY, 2018, 56 (10) : 3136 - 3146
[36] Largest Hosoya Index and Smallest Merrifield-Simmons Index in Tricyclic Graphs
Liu, Yan
Zhuang, Wei
Liang, Zefang
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2015, 73 (01) : 195 - 224
[37] ON THE ORDERING OF A CLASS OF HEXAGONAL CHAINS WITH RESPECT TO MERRIFIELD-SIMMONS INDEX
ZHANG Lianzhu (Department of Mathematics
Systems Science and Mathematical Sciences, 2000, (02) : 219 - 224
[38] The Merrifield-Simmons Index and Hosoya Index of C(n, k, λ) Graphs
Dai, Shaojun
Zhang, Ruihai
JOURNAL OF APPLIED MATHEMATICS, 2012,
[39] On conjecture of Merrifield-Simmons index
Das, Kinkar Chandra
Elumalai, Suresh
Ghosh, Arpita
Mansour, Toufik
DISCRETE APPLIED MATHEMATICS, 2021, 288 (288) : 211 - 217
[40] EXTREMAL VALUES OF MERRIFIELD-SIMMONS INDEX FOR TREES WITH TWO BRANCHING VERTICES
Cruz, Roberto
Marin, Carlos Alberto
Rada, Juan
KRAGUJEVAC JOURNAL OF MATHEMATICS, 2018, 42 (01): : 97 - 106

← 1 2 3 4 5 →