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On the Roman {2}-domatic number of graphs.
- Source :
- Discrete Mathematics, Algorithms & Applications; Oct2021, Vol. 13 Issue 5, p1-10, 10p
- Publication Year :
- 2021
-
Abstract
- Let G = (V , E) be a graph. A Roman { 2 } -dominating function f : V → { 0 , 1 , 2 } has the property 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. A set { f 1 , f 2 , ... , f d } of distinct Roman { 2 } -dominating functions on G with the property that ∑ i = 1 d f i (v) ≤ 2 for each v ∈ V (G) is called a Roman { 2 } -domination family (or functions) on G. The maximum number of functions in a Roman { 2 } -dominating family on G is the Roman { 2 } -domatic number of G , denoted by d { R 2 } (G). In this paper, we answer two conjectures of Volkman [L. Volkmann, The Roman { 2 } -domatic number of graphs, Discrete Appl. Math. 258 (2019) 235–241] about Roman { 2 } -domatic number of graphs and we study this parameter for join of graphs and complete bipartite graphs. [ABSTRACT FROM AUTHOR]
- Subjects :
- DOMINATING set
BIPARTITE graphs
COMPLETE graphs
ROMANS
Subjects
Details
- Language :
- English
- ISSN :
- 17938309
- Volume :
- 13
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 153014673
- Full Text :
- https://doi.org/10.1142/S179383092150052X