Total Roman domination for proper interval graphs
| Main Author: | Poureidi, Abolfazl; Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2020
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/952 https://www.ejgta.org/index.php/ejgta/article/view/952/pdf_149 |
Daftar Isi:
- A function f:V → {0,1,2} is a total Roman dominating function (TRDF) on a graph G=(V,E) if for every vertex v ∈ V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and for every vertex v ∈ V with f(v) > 0 there exists a vertex u ∈ NG(v) with f(u) > 0. The weight of a total Roman dominating function f on G is equal to f(V)=Σv ∈ Vf(v). The minimum weight of a total Roman dominating function on G is called the total Roman domination number of G. In this paper, we give an algorithm to compute the total Roman domination number of a given proper interval graph G=(V,E) in O(|V|) time.