Next Article in Journal
Evaluation of Shear Stress Transport, Large Eddy Simulation and Detached Eddy Simulation for the Flow around a Statically Loaded Tire
Previous Article in Journal
Bilateral Symmetry of Jumping and Agility in Professional Basketball Players: Differentiating Performance Levels and Playing Positions

Quadruple Roman Domination in Trees

Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
College of Science, East China University of Technology, Nanchang 330013, China
College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
Author to whom correspondence should be addressed.
Academic Editor: Juan Luis García Guirao
Symmetry 2021, 13(8), 1318;
Received: 2 July 2021 / Revised: 20 July 2021 / Accepted: 21 July 2021 / Published: 22 July 2021
This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,,k+1} if for any vertex uV with f(u)<k, xN(u){u}f(x)|{xN(u):f(x)1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value ΣvVf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees. View Full-Text
Keywords: quadruple Roman domination; Roman domination; trees quadruple Roman domination; Roman domination; trees
Show Figures

Figure 1

MDPI and ACS Style

Kou, Z.; Kosari, S.; Hao, G.; Amjadi, J.; Khalili, N. Quadruple Roman Domination in Trees. Symmetry 2021, 13, 1318.

AMA Style

Kou Z, Kosari S, Hao G, Amjadi J, Khalili N. Quadruple Roman Domination in Trees. Symmetry. 2021; 13(8):1318.

Chicago/Turabian Style

Kou, Zheng, Saeed Kosari, Guoliang Hao, Jafar Amjadi, and Nesa Khalili. 2021. "Quadruple Roman Domination in Trees" Symmetry 13, no. 8: 1318.

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop