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arXiv · 2107.08263

The Signed (Total) Roman Domination Problem on some Classes of Planar Graphs -- Convex Polytopes

Tatjana Zec·Marko Djukanovic·Dragan Matic
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Abstract

In this paper we deal with the calculation of the signed (total) Roman domination numbers, $γ_{sR}$ and $γ_{stR}$ respectively, on a few classes of planar graphs from the literature. We give proofs for the exact values of the numbers $γ_{sR}(A_n)$ and $γ_{sR}(R_n)$ as well as the numbers $γ_{stR}(S_n)$ and $γ_{stR}(T_n)$. For some other classes of planar graphs, such as $Q_n$, %$S_n"$ and $T_n"$, lower and upper bounds on $γ_{sR}$ are calculated and proved. %We give some open problems on the exact values of $γ_{sR}$ and $γ_{stR}$ for some classes of planar graphs.

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Tatjana Zec, Marko Djukanovic, Dragan Matic. 2021-07-17. The Signed (Total) Roman Domination Problem on some Classes of Planar Graphs -- Convex Polytopes. https://arxiv.org/abs/2107.08263

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