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Total Roman {3}-domination in Graphs.
- Source :
-
Symmetry (20738994) . Feb2020, Vol. 12 Issue 2, p268. 1p. - Publication Year :
- 2020
-
Abstract
- For a graph G = (V , E) with vertex set V = V (G) and edge set E = E (G) , a Roman { 3 } -dominating function (R { 3 } -DF) is a function f : V (G) → { 0 , 1 , 2 , 3 } having the property that ∑ u ∈ N G (v) f (u) ≥ 3 , if f (v) = 0 , and ∑ u ∈ N G (v) f (u) ≥ 2 , if f (v) = 1 for any vertex v ∈ V (G) . The weight of a Roman { 3 } -dominating function f is the sum f (V) = ∑ v ∈ V (G) f (v) and the minimum weight of a Roman { 3 } -dominating function on G is the Roman { 3 } -domination number of G, denoted by γ { R 3 } (G) . Let G be a graph with no isolated vertices. The total Roman { 3 } -dominating function on G is an R { 3 } -DF f on G with the additional property that every vertex v ∈ V with f (v) ≠ 0 has a neighbor w with f (w) ≠ 0 . The minimum weight of a total Roman { 3 } -dominating function on G, is called the total Roman { 3 } -domination number denoted by γ t { R 3 } (G) . We initiate the study of total Roman { 3 } -domination and show its relationship to other domination parameters. We present an upper bound on the total Roman { 3 } -domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. Finally, we investigate the complexity of total Roman { 3 } -domination for bipartite graphs. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BIPARTITE graphs
*GRAPH connectivity
*GEOMETRIC vertices
*ROMANS
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 12
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 142090367
- Full Text :
- https://doi.org/10.3390/sym12020268