Counting the number of dominating sets of cactus chains

被引：0

作者：

Alikhani, S. ^{[1
]}

Jahari, S. ^{[1
]}

Mehryar, M. ^{[1
]}

Hasni, R. ^{[2
]}

机构：

[1] Yazd Univ, Dept Math, Yazd 89195741, Iran

[2] Univ Malaysia Terengganu, Fac Sci & Technol, Dept Math, Kuala Terengganu 21030, Malaysia

来源：

OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS | 2014年 / 8卷 / 9-10期

关键词：

Domination polynomial; Dominating sets; Cactus; HOSOYA INDEX; GRAPH; TREES;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G, x) =Sigma(n)(n=r(g))d(G, i)x(i), where d(G,i) is the number of dominating sets of G of size i and r(G) is the domination number of G. The number of dominating sets of a graph G is D(G,1). In this paper we consider cactus chains with triangular and square blocks and study their domination polynomials.

引用

页码：955 / 960

页数：6

共 50 条

[31] Counting dominating sets in generalized series-parallel graphs
Lin, Min-Sheng
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2019, 11 (06)
[32] DOMINATING SETS AND DOMATIC NUMBER OF CIRCULAR ARC GRAPHS
BONUCCELLI, MA
DISCRETE APPLIED MATHEMATICS, 1985, 12 (03) : 203 - 213
[33] Number of Dominating Sets in Cylindric Square Grid Graphs
Oh, Seungsang
GRAPHS AND COMBINATORICS, 2021, 37 (04) : 1357 - 1372
[34] On the maximum number of minimum total dominating sets in forests
Henning, N. Michael A.
Mohr, Elena
Rautenbach, Dieter
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2019, 21 (03):
[35] Number of Dominating Sets in Cylindric Square Grid Graphs
Seungsang Oh
Graphs and Combinatorics, 2021, 37 : 1357 - 1372
[36] On the number of minimal dominating sets on some graph classes
Couturier, Jean-Francois
Letourneur, Romain
Liedloff, Mathieu
THEORETICAL COMPUTER SCIENCE, 2015, 562 : 634 - 642
[37] An improvement on the maximum number of k-dominating independent sets
Gerbner, Daniel
Keszegh, Balazs
Methuku, Abhishek
Patkos, Balazs
Vizer, Mate
JOURNAL OF GRAPH THEORY, 2019, 91 (01) : 88 - 97
[38] Efficient dominating sets in circulant graphs with domination number prime
Deng, Yun-Ping
INFORMATION PROCESSING LETTERS, 2014, 114 (12) : 700 - 702
[39] Bounding the number of minimal dominating sets: A measure and conquer approach
Fomin, FV
Grandoni, F
Pyatkin, AV
Stepanov, AA
ALGORITHMS AND COMPUTATION, 2005, 3827 : 573 - 582
[40] Enumeration and maximum number of minimal dominating sets for chordal graphs
Golovach, Petr A.
Kratsch, Dieter
Liedtoff, Mathieu
Sayadi, Mohamed Yosri
THEORETICAL COMPUTER SCIENCE, 2019, 783 : 41 - 52

← 1 2 3 4 5 →