On the Italian reinforcement number of a digraph
| Autor: | Shuting Zeng, Zhihong Xie, Guoliang Hao, Seyed Mahmoud Sheikholeslami |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Combinatorics
Domination analysis General Mathematics Digraph Cartesian product directed graph Square (algebra) Physics::History of Physics Combinatorics symbols.namesake italian reinforcement number Mathematics::Algebraic Geometry Computer Science::Discrete Mathematics symbols italian domination number QA1-939 Order (group theory) Physics::Atomic Physics cartesian product Mathematics |
| Zdroj: | AIMS Mathematics, Vol 6, Iss 6, Pp 6490-6505 (2021) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2021382?viewType=HTML |
| Popis: | The Italian reinforcement number of a digraph is the minimum number of arcs that have to be added to the digraph in order to decrease the Italian domination number. In this paper, we present some new sharp upper bounds on the Italian reinforcement number of a digraph. We also determine the exact values of the Italian reinforcement number of the Cartesian products of directed paths and directed cycles: $ P_2\square P_n $, $ P_3\square P_n $, $ P_3\square C_n $, $ C_3\square P_n $ and $ C_3\square C_n $. |
| Databáze: | OpenAIRE |
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