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C O ] 1 7 M ar 2 01 5 Total [ 1 , 2 ]-domination in graphs ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lv, Xuezheng Wu, Baoyindureng |
| Copyright Year | 2018 |
| Abstract | A subset S ⊆ V in a graph G = (V,E) is a total [1, 2]-set if, for every vertex v ∈ V , 1 ≤ |N(v) ∩ S| ≤ 2. The minimum cardinality of a total [1, 2]-set of G is called the total [1, 2]-domination number, denoted by γt[1,2](G). We establish two sharp upper bounds on the total [1,2]-domination number of a graph G in terms of its order and minimum degree, and characterize the corresponding extremal graphs achieving these bounds. Moreover, we give some sufficient conditions for a graph without total [1, 2]-set and for a graph with the same total [1, 2]-domination number, [1, 2]-domination number and domination number. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1503.04939 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
