| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 418547 | Discrete Applied Mathematics | 2011 | 20 Pages |
Let G=(V,E)G=(V,E) be a graph. A set S⊆VS⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in SS and every vertex in V−SV−S is adjacent to a vertex in V−SV−S. The total restrained domination number of GG, denoted γtr(G)γtr(G), is the smallest cardinality of a total restrained dominating set of GG. We will show that if GG is claw-free, connected, has minimum degree at least two and GG is not one of nine exceptional graphs, then γtr(G)≤4n7.
► Let G=(V,E)G=(V,E) be a graph. ► A set S⊆VS⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in SS and every vertex in V−SV−S is adjacent to a vertex in V−SV−S. ► The total restrained domination number of GG, denoted γtr(G)γtr(G), is the smallest cardinality of a total restrained dominating set of GG. ► We will show that if GG is claw-free, connected, has minimum degree at least two and GG is not one of nine exceptional graphs, then γtr(G)≤4n7.
