On Double Roman Dominating Functions in Graphs

Authors

  • Jerry Boy Cariaga Mindanao State University- Iligan Institute of Technology
  • Ferdinand Jamil

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4653

Keywords:

Domination number, 2-domination number, double Roman dominating function, double Roman domination number

Abstract

Let $G$ be a connected graph. A function $f:V(G)\to \{0,1,2,3\}$ is a double Roman dominating function of $G$ if for each $v\in V(G)$ with $f(v)=0$, $v$ has two adjacent vertices $u$ and $w$ for which $f(u)=f(w)=2$ or $v$ has an adjacent vertex $u$ for which $f(u)=3$, and for each $v\in V(G)$ with $f(v)=1$, $v$ is adjacent to a vertex $u$ for which either $f(u)=2$ or $f(u)=3$. The minimum weight $\omega_G(f)=\sum_{v\in V(G)}f(v)$ of a double Roman dominating function $f$ of $G$ is the double Roman domination number of $G$. In this paper, we continue the study of double Roman domination introduced and studied by R.A. Beeler et al. in [2]. First, we characterize some double Roman domination numbers with small values in terms of the domination numbers and 2-domination numbers. Then we determine the double Roman domination numbers of the join, corona, complementary prism and lexicographic product of graphs.

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Published

2023-04-30

Issue

Section

Nonlinear Analysis

How to Cite

On Double Roman Dominating Functions in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(2), 847-863. https://doi.org/10.29020/nybg.ejpam.v16i2.4653

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