Total k-domination in strong product graphs

被引：12

作者：

Bermudo, S. ^{[1
]}

Hernandez-Gomez, J. C. ^{[2
]}

Sigarreta, J. M. ^{[2
]}

机构：

[1] Univ Pablo Olavide, Dept Econ Quantitat Methods & Econ Hist, ES-41013 Seville, Spain

[2] Autonomous Univ Guerrero, Fac Math, Carlos E Adame 5, Acapulco, Guerrero, Mexico

来源：

DISCRETE APPLIED MATHEMATICS | 2019年 / 263卷

关键词：

k-domination; Domination; Total domination; k-tuple domination; NUMBER;

D O I：

10.1016/j.dam.2018.03.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G = (V, E) be a graph, a set S subset of V is a total k-dominating set if every vertex upsilon is an element of E V has at least k neighbors in S. The total k-domination number y(kt)(G) is the minimum cardinality among all total k-dominating sets. In this paper, we obtain several tight bounds for the total k-domination number of the strong product of two graphs. In particular, we investigate the relationship between the total k-domination number of the strong product of two graphs with the domination, k-domination and total k-domination numbers of the factors in the product. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：51 / 58

页数：8

共 22 条

[1] Total k-domination in Cartesian product graphs [J].

Bermudo, S. ;

Sanchez, J. L. ;

Sigarreta, J. M. .

PERIODICA MATHEMATICA HUNGARICA, 2017, 75 (02) :255-267

[2]

Bermudo S., UTIL MATH

[3] ON THE TOTAL k-DOMINATION IN GRAPHS [J].

Bermudo, Sergio ;

Hernandez-Gomez, Juan C. ;

Sigarreta, Jose M. .

DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2018, 38 (01) :301-317

[4]

Brigham R.C., 2000, J COMBIN COMPUT COMB, V34, P81

[5] Toughness of the corona of two graphs [J].

Casablanca, R. M. ;

Dianez, A. ;

Garica-Vazquez, P. .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2011, 88 (13) :2697-2706

[6] TOTAL DOMINATION IN GRAPHS [J].

COCKAYNE, EJ ;

DAWES, RM ;

HEDETNIEMI, ST .

NETWORKS, 1980, 10 (03) :211-219

[7] AN UPPER BOUND FOR THE K-DOMINATION NUMBER OF A GRAPH [J].

COCKAYNE, EJ ;

GAMBLE, B ;

SHEPHERD, B .

JOURNAL OF GRAPH THEORY, 1985, 9 (04) :533-534

[8] On the total domination number of cross products of graphs [J].

Ei-Zahar, Mohamed ;

Gravier, Sylvain ;

Klobucar, Antoaneta .

DISCRETE MATHEMATICS, 2008, 308 (10) :2025-2029

[9]

Fernau H, 2015, UTILITAS MATHEMATICA, V98, P127

[10]

Fink J. F., 1985, Periodica Mathematica Hungarica, V16, P287, DOI 10.1007/BF01848079

← 1 2 3 →