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New bounds on the outer-independent total double Roman domination number.
- Source :
-
Discrete Mathematics, Algorithms & Applications . May2024, Vol. 16 Issue 4, p1-13. 13p. - Publication Year :
- 2024
-
Abstract
- A double Roman dominating function (DRDF) on a graph G = (V , E) is a function f : V → { 0 , 1 , 2 , 3 } satisfying (i) if f (v) = 0 then there must be at least two neighbors assigned two under f or one neighbor w with f (w) = 3 ; and (ii) if f (v) = 1 then v must be adjacent to a vertex w such that f (w) ≥ 2. A DRDF is an outer-independent total double Roman dominating function (OITDRDF) on G if the set of vertices labeled 0 induces an edgeless subgraph and the subgraph induced by the vertices with a non-zero label has no isolated vertices. The weight of an OITDRDF is the sum of its function values over all vertices, and the outer-independent total Roman domination number γ tdR oi (G) is the minimum weight of an OITDRDF on G. In this paper, we establish various bounds on γ tdR oi (G). In particular, we present Nordhaus–Gaddum-type inequalities for this parameter. Some of our results improve the previous results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DOMINATING set
*ROMANS
*NEIGHBORS
Subjects
Details
- Language :
- English
- ISSN :
- 17938309
- Volume :
- 16
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 176610544
- Full Text :
- https://doi.org/10.1142/S179383092350043X