Global italian domination in graphs. Issue 8 (8th October 2019)
- Record Type:
- Journal Article
- Title:
- Global italian domination in graphs. Issue 8 (8th October 2019)
- Main Title:
- Global italian domination in graphs
- Authors:
- Hao, Guoliang
Hu, Kangxiu
Wei, Shouliu
Xu, Zhijun - Abstract:
- Abstract: 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 ( G ) 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. The weight of an IDF f is the value ∑ v∈V ( G ) f ( v ). The Italian domination number of a graph G, denoted by γI (G), is the minimum weight of an IDF on G . An IDF f on G is called a global Italian dominating function (GIDF) on G if f is also an IDF on the complement Ḡ of G . The global Italian domination number of G, denoted by γgI ( G ), is the minimum weight of a GIDF on G . In this paper, we initiate the study of the global Italian domination number and we present some strict bounds for the global Italian domination number. In particular, we prove that for any tree T of order n ≥ 4, γgI ( T) ≤ γI ( T) + 2 and we characterize all trees with γgI ( T) = γI ( T) + 2 and γgI ( T) = γI ( T) + 1.
- Is Part Of:
- Quaestiones mathematicae. Volume 42:Issue 8(2019)
- Journal:
- Quaestiones mathematicae
- Issue:
- Volume 42:Issue 8(2019)
- Issue Display:
- Volume 42, Issue 8 (2019)
- Year:
- 2019
- Volume:
- 42
- Issue:
- 8
- Issue Sort Value:
- 2019-0042-0008-0000
- Page Start:
- 1101
- Page End:
- 1115
- Publication Date:
- 2019-10-08
- Subjects:
- 05C69
Italian dominating function -- Italian domination number -- global Italian dominating function -- global Italian domination number
Mathematics -- Periodicals
510.5 - Journal URLs:
- http://www.nisc.co.za/journals?id=7 ↗
http://www.tandfonline.com/loi/tqma20 ↗
http://www.tandfonline.com/ ↗
http://www.ingentaconnect.com/content/nisc/qm? ↗ - DOI:
- 10.2989/16073606.2018.1506831 ↗
- Languages:
- English
- ISSNs:
- 1607-3606
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 7168.117400
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 11866.xml