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arXiv · 1908.06859

Impact of Some Graph Operations on Double Roman Domination Number

Anu V.·Aparna Lakshmanan S.
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Abstract

Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\in N(v)$ such that $f(v_{1})=f(v_{2})=2$ or there exists $ w \in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then there exists $ w \in N(v)$ such that $f(w)\geq 2$ is called a double Roman dominating function (DRDF). The weight of a DRDF $f$ is the sum $f(V)=\sum_{v\in V}f(v)$. The double Roman domination number, $\gamma_{dR}(G)$, is the minimum among the weights of DRDFs on $G$. In this paper, we study the impact of some graph operations, such as cartesian product, addition of twins and corona with a graph, on double Roman domination number.

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Anu V., Aparna Lakshmanan S.. 2019-08-19. Impact of Some Graph Operations on Double Roman Domination Number. https://arxiv.org/abs/1908.06859

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