Author, as appears in the article.: Cabrera Martinez, Abel; Cabrera Garcia, Suitberto; Carrion Garcia, Andres; Hernandez Mira, Frank A.;
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: CABRERA MARTÍNEZ, ABEL
Keywords: Total roman domination Total domination Rooted product graph
Abstract: Let G be a graph with no isolated vertex and f:V(G)->{0,1,2} a function. If f satisfies that every vertex in the set {v is an element of V(G):f(v)=0} is adjacent to at least one vertex in the set {v is an element of V(G):f(v)=2}, and if the subgraph induced by the set {v is an element of V(G):f(v)>= 1} has no isolated vertex, then we say that f is a total Roman dominating function on G. The minimum weight omega(f)= n-ary sumation v is an element of V(G)f(v) among all total Roman dominating functions f on G is the total Roman domination number of G. In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the total Roman domination number of rooted product graphs in terms of domination invariants of the factor graphs involved in this product.
Thematic Areas: Química Mathematics (miscellaneous) Mathematics General mathematics Astronomia / física
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: abel.cabrera@urv.cat
Author identifier: 0000-0003-2806-4842
Record's date: 2021-10-10
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: https://www.mdpi.com/2227-7390/8/10/1850
Papper original source: Mathematics. 8 (10): 1-13
APA: Cabrera Martinez, Abel; Cabrera Garcia, Suitberto; Carrion Garcia, Andres; Hernandez Mira, Frank A.; (2020). Total Roman Domination Number of Rooted Product Graphs. Mathematics, 8(10), 1-13. DOI: 10.3390/math8101850
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Article's DOI: 10.3390/math8101850
Entity: Universitat Rovira i Virgili
Journal publication year: 2020
Publication Type: Journal Publications
Repositori URV