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
Article

Quadruple Roman Domination in Trees

1
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
2
College of Science, East China University of Technology, Nanchang 330013, China
3
College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
4
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; https://doi.org/10.3390/sym13081318
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. https://doi.org/10.3390/sym13081318

AMA Style

Kou Z, Kosari S, Hao G, Amjadi J, Khalili N. Quadruple Roman Domination in Trees. Symmetry. 2021; 13(8):1318. https://doi.org/10.3390/sym13081318

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. https://doi.org/10.3390/sym13081318

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

1
Back to TopTop