%0 Journal Article 
%A Ahangar, H.A.
%A Chellali, M.
%A Sheikholeslami, S.M.
%A Valenzuela Tripodoro, Juan Carlos
%T Total Roman {2}-Domination in Graphs
%D 2020
%@ 1234-3099
%U http://hdl.handle.net/10498/24377
%X A Roman {2}-dominating function (R2F) is a function f: V → {0, 1, 2} with the property that for every vertex v â V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1. A total Roman {2}-dominating function (TR2DF) is an R2F f such that the set of vertices with f(v) > 0 induce a subgraph with no isolated vertices. The weight of a TR2DF is the sum of its function values over all vertices, and the minimum weight of a TR2DF of G is the total Roman {2}-domination number γtR2(G). In this paper, we initiate the study of total Roman {2}-dominating functions, where properties are established. Moreover, we present various bounds on the total Roman {2}-domination number. We also show that the decision problem associated with γtR2(G) is possible to compute this parameter in linear time for bounded clique-width graphs (including trees). © 2020 H. Abdollahzadeh Ahangar et al., published by Sciendo 2020.
%K Roman {2}
%K Roman {2}-domination
%K total Roman {2}- domination
%~ Universidad de Cádiz