Weak signed double Roman domination in graphs

Document Type : Original paper

Author

RWTH Aachen University, 52056 Aachen, Germany

Abstract

A weak signed double Roman dominating function (WSDRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2,3\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSDRDF is the sum of its function values over all vertices. The weak signed double Roman domination number of $G$, denoted by $\gamma_{wsdR}(G)$, is the minimum weight of a WSDRDF in $G$. We initiate the study of the weak signed double Roman domination number, and we present different sharp bounds on $\gamma_{wsdR}(G)$. In addition, we determine the weak signed double Roman domination number of some classes of graphs.

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References

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https://doi.org/10.22049/cco.2021.26998.1178
Communications in Combinatorics and Optimization
Volume 11, Issue 3
September 2026
Pages 739-756

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