Italian Reinforcement Number in Graphs
An Italian dominating function (IDF) on a graph G = (V, E) is a function f:V → {0, 1, 2} satisfying the condition that for every vertex v ∈ V with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1 under f. The weig...
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doaj-085f9f1e95fd4383ab6a9fe75097aa232021-03-29T23:14:10ZengIEEEIEEE Access2169-35362019-01-01718444818445610.1109/ACCESS.2019.29603908935253Italian Reinforcement Number in GraphsGuoliang Hao0https://orcid.org/0000-0002-1267-696XSeyed Mahmoud Sheikholeslami1https://orcid.org/0000-0003-2298-4744Shouliu Wei2https://orcid.org/0000-0002-1723-5186College of Science, East China University of Technology, Nanchang, ChinaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranCollege of Mathematics and Data Science, Minjiang University, Fuzhou, ChinaAn Italian dominating function (IDF) on a graph G = (V, E) is a function f:V → {0, 1, 2} satisfying the condition that for every vertex v ∈ V with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1 under f. The weight of an IDF f is the value Σ<sub>v∈V</sub>f(v). The Italian domination number of a graph G is the minimum weight of an IDF on G. The Italian reinforcement number of a graph is the minimum number of edges that have to be added to the graph in order to decrease the Italian domination number. In this paper, we initiate the study of Italian reinforcement number and we present some sharp upper bounds for this parameter. In particular, we determine the exact Italian reinforcement numbers of some classes of graphs.https://ieeexplore.ieee.org/document/8935253/Italian domination numberItalian reinforcement numberCartesian product |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Guoliang Hao Seyed Mahmoud Sheikholeslami Shouliu Wei |
spellingShingle |
Guoliang Hao Seyed Mahmoud Sheikholeslami Shouliu Wei Italian Reinforcement Number in Graphs IEEE Access Italian domination number Italian reinforcement number Cartesian product |
author_facet |
Guoliang Hao Seyed Mahmoud Sheikholeslami Shouliu Wei |
author_sort |
Guoliang Hao |
title |
Italian Reinforcement Number in Graphs |
title_short |
Italian Reinforcement Number in Graphs |
title_full |
Italian Reinforcement Number in Graphs |
title_fullStr |
Italian Reinforcement Number in Graphs |
title_full_unstemmed |
Italian Reinforcement Number in Graphs |
title_sort |
italian reinforcement number in graphs |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2019-01-01 |
description |
An Italian dominating function (IDF) on a graph G = (V, E) is a function f:V → {0, 1, 2} satisfying the condition that for every vertex v ∈ V with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1 under f. The weight of an IDF f is the value Σ<sub>v∈V</sub>f(v). The Italian domination number of a graph G is the minimum weight of an IDF on G. The Italian reinforcement number of a graph is the minimum number of edges that have to be added to the graph in order to decrease the Italian domination number. In this paper, we initiate the study of Italian reinforcement number and we present some sharp upper bounds for this parameter. In particular, we determine the exact Italian reinforcement numbers of some classes of graphs. |
topic |
Italian domination number Italian reinforcement number Cartesian product |
url |
https://ieeexplore.ieee.org/document/8935253/ |
work_keys_str_mv |
AT guolianghao italianreinforcementnumberingraphs AT seyedmahmoudsheikholeslami italianreinforcementnumberingraphs AT shouliuwei italianreinforcementnumberingraphs |
_version_ |
1724189833555869696 |