On the Italian reinforcement number of a digraph

Zhihong Xie; Guoliang Hao; S. M. Sheikholeslami; Shuting Zeng; Zhihong Xie; Guoliang Hao; S. M. Sheikholeslami; Shuting Zeng

doi:10.3934/math.2021382

AIMS Mathematics

2021, Volume 6, Issue 6: 6490-6505. doi: 10.3934/math.2021382

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Research article

On the Italian reinforcement number of a digraph

1.
College of Science, East China University of Technology, Nanchang 330013, China
2.
College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
3.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Received: 16 January 2021 Accepted: 12 April 2021 Published: 15 April 2021
MSC : 05C69, 05C20

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 $.
- Italian domination number,
- Italian reinforcement number,
- Cartesian product,
- directed graph
Citation: Zhihong Xie, Guoliang Hao, S. M. Sheikholeslami, Shuting Zeng. On the Italian reinforcement number of a digraph[J]. AIMS Mathematics, 2021, 6(6): 6490-6505. doi: 10.3934/math.2021382

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Abstract

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 $.

References

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