Weak signed total Italian domination in graphs

Document Type : Original paper

Author

RWTH Aachen University, 52056 Aachen, Germany

Abstract

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

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References

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Communications in Combinatorics and Optimization
Volume 12, Issue 1
March 2027
Pages 283-296

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