Weak signed total Italian domination in graphs

Articles in Press

Document Type : Original paper

Author

RWTH Aachen University

Abstract

A {\em 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 {\em 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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Main Subjects

Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 21 March 2025

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