On the total Italian domination number in digraphs
Changchang Dong, Yubao Guo, Mei Lu, Lutz Volkmann

TL;DR
This paper introduces the concept of total Italian domination in digraphs, establishes bounds for this parameter, and computes it explicitly for Cartesian products of paths, advancing understanding of domination parameters in directed graphs.
Contribution
It defines the total Italian domination number for digraphs, provides bounds, and calculates exact values for specific Cartesian product digraphs, extending domination theory.
Findings
Bounds on the total Italian domination number are established.
Exact values are computed for Cartesian products P2×Pn and P3×Pn.
The relationship between total Italian domination and other parameters is analyzed.
Abstract
Consider a finite simple digraph with vertex set . An Italian dominating function (IDF) on is a function satisfying every vertex with has an in-neighbor with or two in-neighbors and with . A total Italian dominating function (TIDF) on is an IDF such that the subdigraph contains no isolated vertices. The weight of a TIDF on is . The total Italian domination number of is \gamma_{tI}(D)=\min\{ \omega(f)\, |\, \mbox{fD}\}. In this paper, we present bounds on , and investigate the relationship between several different domination parameters. In particular, we give the total Italian domination number of the Cartesian products and , where represents a…
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research
