学术期刊
切换导航
首 页
文 章
期 刊
投 稿
预 印
会 议
书 籍
新 闻
合 作
我 们
按学科分类
Journals by Subject
按期刊分类
Journals by Title
核心OA期刊
Core OA Journal
数学与物理
Math & Physics
化学与材料
Chemistry & Materials
生命科学
Life Sciences
医药卫生
Medicine & Health
信息通讯
Information & Communication
工程技术
Engineering & Technology
地球与环境
Earth & Environment
经济与管理
Economics & Management
人文社科
Humanities & Social Sciences
合作期刊
Cooperation Journals
首页
数学与物理
应用数学进展
Vol. 5 No. 3 (August 2016)
期刊菜单
最新文章
历史文章
检索
领域
编委
投稿须知
文章处理费
最新文章
历史文章
检索
领域
编委
投稿须知
文章处理费
关于
C
m
×
P
k
的反强迫数
On the Anti-Forcing Number of
C
m
×
P
k
DOI:
10.12677/AAM.2016.53054
,
PDF
,
HTML
,
XML
,
被引量
下载: 2,268
浏览: 6,217
作者:
张勇军
,
蔡金转
*
:海南大学数学系,海南 海口
关键词:
圈和路的卡什积图
;
完美匹配
;
反强迫数
;
The Cartesian Product of a Cycle and a Path
;
Perfect Matching
;
Anti-Forcing Numbers
摘要:
设
G
是一个有完美匹配的简单连通图。若
G
的一个边子集
S
满足
G
-
S
只有唯一完美匹配,则称
S
是
G
的一个反强迫集。
G
中最小的反强迫集的大小称为
G
的反强迫数。本文主要研究圈和路的卡什积图的反强迫数。根据一个图有唯一完美匹配的必要条件,我们证明了
C
3
×
P
2k
,
C
2K+1
×
P
2
,
C
4
×
P
的反强迫数都为
k+1
,并表明了
C
2k
×
P
2
(k≥2) 的反强迫数恒为3。
Abstract:
Let
G
be a simple connected graph with a perfect matching,
S
an edge set of
G
. We call
S
an anti- forcing set of
G
, if
G
-
S
contains only one perfect matching of
G
. The cardinality of the minimum anti-forcing set of
G
is called the anti-forcing number of
G
. In this paper, we study the anti-forcing number of the Cartesian product of a cycle and a path. According to the necessity of a graph with only one perfect matching, we show that the anti-forcing numbers of
C
3
×
P
2k
,
C
2K+1
×
P
2
,
C
4
×
P
are all
k+1
, and the anti-forcing number of
C
2k
×
P
2
(k≥2) is 3.
文章引用:
张勇军, 蔡金转. 关于
C
m
×
P
k
的反强迫数[J]. 应用数学进展, 2016, 5(3): 435-442.
http://dx.doi.org/10.12677/AAM.2016.53054
参考文献
[
1
]
Klein, D. and Randic, M. (1987) Innate Degree of Freedom of a Graph. Journal of Computational Chemistry, 8, 516-521.
http://dx.doi.org/10.1002/jcc.540080432
[
2
]
Randic, M. and Klein, D. (1985) Kekule Valence Structures Revisited. Innate Degrees of Freedom of π-Electron Couplings. In: Trinajstic, N., Ed., Mathematics and Computational Concepts in Chemistry, Hor-wood/Wiley, New York, 274-282.
[
3
]
Harary, F., Klein, D. and Zivkovic, T. (1991) Graphical Properties of Polyhexes: Perfect Matching Vector and Forcing. Journal of Mathematical Chemistry, 6, 295-306.
http://dx.doi.org/10.1007/BF01192587
[
4
]
Vukicevic, D. and Trinajstic, N. (2007) On the Anti-Forcing Number of Benzenoids. Journal of Mathematical Chemistry, 42, 575-583.
http://dx.doi.org/10.1007/s10910-006-9133-6
[
5
]
Deng, H. (2007) The Anti-Forcing Number of Hexagonal Chains. MATCH Communications in Mathematical and in Computer Chemistry, 58, 675-682.
[
6
]
Deng, H. (2008) The Anti-Forcing Number of Double Hexagonal Chains. MATCH Communications in Mathematical and in Computer Chemistry, 60, 183-192.
[
7
]
Zhang, Q., Bian, H. and Vumar, E. (2011) On the Anti-Kekule and Anti-Forcing Number of Cata-Condensed phenylenes. MATCH Communications in Mathematical and in Computer Chemistry, 65, 799-806.
[
8
]
杨琴. 富勒烯图的反凯库勒数和反强迫数[D]: [硕士学位论文]. 兰州: 兰州大学, 2010.
[
9
]
蒋晓艳, 程晓胜. 硼氮富勒烯图的反强迫数[J]. 湖北师范学院学报(自然科学版), 2013, 33(3): 28-30.
[
10
]
Lovasz, L. and Plummer, M.D. (1986) Matching Theory. Annals of Discrete Mathematics Vol. 29, North-Holland, Amsterdam.
投稿
为你推荐
友情链接
科研出版社
开放图书馆