Article in volume
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Title:
Bounds on the total double Roman domination number of graphs
PDFSource:
Discussiones Mathematicae Graph Theory 43(4) (2023) 1033-1061
Received: 2020-11-03 , Revised: 2021-06-06 , Accepted: 2021-06-07 , Available online: 2021-06-25 , https://doi.org/10.7151/dmgt.2417
Abstract:
Let $G$ be a simple graph with no isolated vertex and let $\gamma_{tdR}(G)$ be
the total double Roman domination number of $G$. In this paper, we present lower
and upper bounds on $\gamma_{tdR}(G)$ of a graph $G$ in terms of the order, open
packing number and the numbers of support vertices and leaves, and we
characterize all extremal graphs. We also prove that for any connected graph $G$
of order $n$ with minimum degree at least two, $\gamma_{tdR}({G})\le\left\lfloor
\frac{4n}{3}\right\rfloor$.
Keywords:
double Roman domination, total double Roman domination, open packing
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