Author, as appears in the article.: Martinez, Abel Cabrera; Peterin, Iztok; Yero, Ismael G.;

Department: Enginyeria Informàtica i Matemàtiques

URV's Author/s: CABRERA MARTÍNEZ, ABEL

Keywords: Rooted product graph Roman domination Paths Number Extremal problems Domination Direct product graph Cardinal product

Abstract: Let G be a graph with vertex set V(G). A function f : V(G) -> {0, 1, 2) is a Roman dominating function on G if every vertex v is an element of V(G) for which f(v) = 0 is adjacent to at least one vertex u is an element of V(G) such that f(u) = 2. The Roman domination number of G is the minimum weight omega(f) = Sigma(x is an element of V(G)) f(x) among all Roman dominating functions f on G. In this article we study the Roman domination number of direct product graphs and rooted product graphs. Specifically, we give several tight lower and upper bounds for the Roman domination number of direct product graphs involving some parameters of the factors, which include the domination, (total) Roman domination, and packing numbers among others. On the other hand, we prove that the Roman domination number of rooted product graphs can attain only three possible values, which depend on the order, the domination number, and the Roman domination number of the factors in the product. In addition, theoretical characterizations of the classes of rooted product graphs achieving each of these three possible values are given.

Thematic Areas: Mathematics, applied Mathematics (miscellaneous) Mathematics General mathematics Ciencias sociales

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

Journal volume: 6

Papper version: info:eu-repo/semantics/publishedVersion

Link to the original source: http://www.aimspress.com/article/doi/10.3934/math.2021643

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

Papper original source: Aims Mathematics. 6 (10): 11084-11096

APA: Martinez, Abel Cabrera; Peterin, Iztok; Yero, Ismael G.; (2021). Roman domination in direct product graphs and rooted product graphs1. Aims Mathematics, 6(10), 11084-11096. DOI: 10.3934/math.2021643

Article's DOI: 10.3934/math.2021643

Entity: Universitat Rovira i Virgili

Journal publication year: 2021

Publication Type: Journal Publications