Abstract
Let G = (V, E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S, and every vertex in V − S is adjacent to a vertex in V −S. The total restrained domination number of G, denoted by γtr (G), is the smallest cardinality of a total restrained dominating set of G. In this paper we show that if G is a graph of order n ≥ 4, then (Formula Presented.). We also characterize the graphs achieving the upper bound.
| Original language | English |
|---|---|
| Pages (from-to) | 297-308 |
| Number of pages | 12 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 70 |
| Issue number | 3 |
| Publication status | Published - 2018 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics