On the Secure Total Domination Number of Graphs

Symmetry

Abel Cabrera Martínez¹  JuanA. Rodríguez-Velázquez¹  LuisP. Montejano² 

[1] Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain;Euncet University Business School, Universitat Politècnica de Catalunya, 08225 Terrassa, Spain;

关键词: secure total domination;    secure domination;    independence number;    matching number;    domination;   

DOI  :  10.3390/sym11091165

来源: DOAJ

【 摘 要 】

A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex $u\in V\left(G\right)\backslash D$ , there exists a vertex $v\in D$ , which is adjacent to u, such that $(D\backslash \{v\left\}\right)\cup \left\{u\right\}$ 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.

【 授权许可】

Unknown