Power domination of the cartesian product of graphs

被引：12

作者：

Koh, K. M. ^{[1
]}

Soh, K. W. ^{[1
]}

机构：

[1] Natl Univ Singapore, Dept Math, Lower Kent Ridge Rd, Singapore 119260, Singapore

来源：

AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS | 2016年 / 13卷 / 01期

关键词：

Power domination; Cartesian product; Vizing's Inequality; Corona;

D O I：

10.1016/j.akcej.2016.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs is a tree. (C) 2016 Publishing Services by Elsevier B.V. on behalf of Kalasalingam University.

引用

页码：22 / 30

页数：9

共 10 条

[1] Power Domination in Cylinders, Tori, and Generalized Petersen Graphs [J].

Barrera, Roberto ;

Ferrero, Daniela .

NETWORKS, 2011, 58 (01) :43-49

[2]

Dean N., 2011, Proceedings of the 2011 IEEE 14th International Conference on Computational Science and Engineering (CSE 2011). 11th International Symposium on Pervasive Systems, Algorithms, Networks (I-SPAN 2011). 10th IEEE International Conference on Ubiquitous Computing and Communications (IUCC 2011), P488, DOI 10.1109/CSE.2011.89

[3] Power domination in product graphs [J].

Dorbec, Paul ;

Mollard, Michel ;

Klavzar, Sandi ;

Spacapan, Simon .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2008, 22 (02) :554-567

[4] A note on power domination in grid graphs [J].

Dorfling, M ;

Henning, MA .

DISCRETE APPLIED MATHEMATICS, 2006, 154 (06) :1023-1027

[5] Domination in graphs applied to electric power networks [J].

Haynes, TW ;

Hedetniemi, SM ;

Hedetniemi, ST ;

Henning, MA .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2002, 15 (04) :519-529

[6]

MILI L, 1991, P EPRI NSF WORKSH AP

[7]

Pai K.-J., 2012, 29 WORKSH COMB MATH, P56

[8]

Soh KW, 2014, AKCE INT J GRAPHS CO, V11, P51

[9]

Vizing V.G., 1968, USPEKHIMAT NAUK, V23, P117

[10]

Zhao Min, 2007, Journal of Shanghai University, V11, P218, DOI 10.1007/s11741-007-0305-3

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