On the Secure Total Domination Number of Graphs

被引：5

作者：

Cabrera Martinez, Abel ^{[1
]}

Montejano, Luis P. ^{[2
]}

Rodriguez-Velazquez, Juan A. ^{[1
]}

机构：

[1] Univ Rovira & Virgili, Dept Engn Informat & Matemat, Ave Paisos Catalans 26, E-43007 Tarragona, Spain

[2] Univ Politecn Cataluna, Euncet Univ Business Sch, Terrassa 08225, Spain

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 09期

关键词：

secure total domination; secure domination; independence number; matching number; domination; OUTER-CONNECTED DOMINATION; PROTECTION; ROMAN;

D O I：

10.3390/sym11091165

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u is an element of V(G) \ D, there exists a vertex v is an element of D, which is adjacent to u, such that (D \ {v}) boolean OR {u} is a total dominating set as well. The secure total domination number of G is the minimum cardinality among all secure total dominating sets of G. In this article, we obtain new relationships between the secure total domination number and other graph parameters: namely the independence number, the matching number and other domination parameters. Some of our results are tight bounds that improve some well-known results.

引用

页数：12

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