On Double Roman Dominating Functions in Graphs


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




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


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.






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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