Weak signed total Italian domination in digraphs

Articles in Press

Document Type : Original paper

Author

RWTH Aachen University, , 52056 Aachen, Germany

Abstract

A weak signed total Italian dominating function (WSTIDF) of a digraph $D$ with vertex set $V(D)$ is defined as a
function $f:V(D)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N^-(v)}f(x)\ge 1$ for each $v\in V(D)$, where $N^-(v)$ consists of all vertices of $D$ from which arcs go into $v$. The weight of a WSTIDF is the sum of its function values over all vertices. The  weak signed total Italian domination number of $D$, denoted by $\gamma_{wstI}(D)$, is the minimum weight of a WSTIDF on $D$. We initiate the study of the weak signed total Italian domination number in digraphs, and we  present different sharp bounds on $\gamma_{wstI}(D)$. In addition, we determine the weak signed total Italian domination number of some classes of digraphs.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 14 October 2025

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