Weak signed total double Roman $k$-domination number of graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran

2 Institute for Geometry and Practical Mathematics, RWTH Aachen University, 52056 Aachen,Germany

Abstract

Let $k\ge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$. A weak signed total double Roman $k$-dominating function (WSTDRkDF) on a graph $G$ is defined as a function $f \colon V(G)\rightarrow\{-1,1,2,3\}$ satisfying the conditions that $\sum_{x\in N(v)}f(x)\ge k$ for each vertex $v\in V(G)$, where $N(v)$ is the neighborhood of $v$. The weight of a WSTDRkDF $f$ is $\omega(f)=\sum_{v\in V(G)}f(v)$. The weak signed total double Roman $k$-domination number $\gamma_{wstdR}^k(G)$ of $G$ is the minimum weight among all WSTDRkDF on $G$. In this paper we initiate the study of the weak signed total double Roman $k$-domination number of graphs, and we present different sharp bounds on $\gamma_{wstdR}^k(G)$. In addition, we determine the weak signed total double Roman $k$-domination number of some classes of graphs.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 06 September 2026

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