Author, as appears in the article.: Cabrera A; Kuziak D; Peterin I; Yero IG

Department: Enginyeria Informàtica i Matemàtiques

URV's Author/s: CABRERA MARTÍNEZ, ABEL

Keywords: Total roman domination Roman domination Number Direct product graphs msc: 05c69 Direct product graphs 05c76

Abstract: © 2020 by the authors. Given a graph G without isolated vertices, a total Roman dominating function for G is a function f: V(G) → [0, 1, 2] such that every vertex u with f (u) = 0 is adjacent to a vertex v with f (v) = 2, and the set of vertices with positive labels induces a graph of minimum degree at least one. The total Roman domination number γtR(G) of G is the smallest possible value of ΣvεV(G) f (v) among all total Roman dominating functions f . The total Roman domination number of the direct product G× H of the graphs G and H is studied in this work. Specifically, several relationships, in the shape of upper and lower bounds, between γtR(G× H) and some classical domination parameters for the factors are given. Characterizations of the direct product graphs G× H achieving small values (≤ 7) for γtR(G× H) are presented, and exact values for γtR(G× H) are deduced, while considering various specific direct product classes.

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/2227-7390/8/9/1438

Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/

Papper original source: Mathematics. 8 (9):

APA: Cabrera A; Kuziak D; Peterin I; Yero IG (2020). Dominating the direct product of two graphs through total Roman strategies. Mathematics, 8(9), -. DOI: 10.3390/MATH8091438

Article's DOI: 10.3390/MATH8091438

Entity: Universitat Rovira i Virgili

Journal publication year: 2020

Publication Type: Journal Publications