Total Roman Domination in Graphs

Applicable Analysis and Discrete Mathematics

article

Hossein Abdollahzadeh Ahangar¹  Michael A. Henning²  Vladimir Samodivkin³  Ismael G. Yero⁴ 

[1] Department of Basic Science, Babol Noshirvani University of Technology;Department of Pure and Applied Mathematics University of Johannesburg;Department of Mathematics, University of Architecture, Civil Engineering and Geodesy;Departamento de Matem´aticas, EPS, Universidad de C´adiz Av. Ram´on Puyol

关键词: Roman domination;    Total Roman domination;    Total domination;    Domination;   

DOI  :  10.2298/AADM160802017A

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2}satisfying the condition that every vertex u for which f(u) = 0 is adjacent toat least one vertex v for which f(v) = 2. The weight of a Roman dominatingfunction f is the sum, Pu∈V (G)f(u), of the weights of the vertices. TheRoman domination number is the minimum weight of a Roman dominatingfunction in G. A total Roman domination function is a Roman dominatingfunction with the additional property that the subgraph of G induced by theset of all vertices of positive weight has no isolated vertex. The total Romandomination number is the minimum weight of a total Roman dominationfunction on G. We establish lower and upper bounds on the total Romandomination number. We relate the total Roman domination to dominationparameters, including the domination number, the total domination numberand Roman domination number.

【 授权许可】

Unknown