A characterization of (γt, γ2)-trees

@article{Hou2010ACO,
  title={A characterization of ($\gamma$t, $\gamma$2)-trees},
  author={Xinmin Hou and Ning Li and You Lu and Junming Xu},
  journal={Discuss. Math. Graph Theory},
  year={2010},
  volume={30},
  pages={425-435}
}
Let t(G) and 2(G) be the total domination number and the 2domination number of a graph G, respectively. It has been shown that: t(T ) 2(T ) for any tree T . In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number. 
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k-Domination and k-Independence in Graphs: A Survey

TLDR
This paper surveys results on k-domination and k-independence in graphs with positive integer k.

References

SHOWING 1-10 OF 17 REFERENCES

A characterization of (γ, i)-trees

We characterize trees with equal domination and independent domination numbers in terms of the sets of vertices of the tree which are contained in all its minimum dominating and minimum independent

A characterization of (2, p )-trees

Let G = (V , E) be a graph. A set S ⊆ V is a dominating set of G if every vertex not in S is adjacent with some vertex in S. The domination number of G, denoted by (G), is the minimum cardinality of

Strong equality of domination parameters in trees

Characterizations of trees with equal paired and double domination numbers

On Total Domination in Graphs

LetG = (V,E) be a finite, simple, undirected graph. A set S ⊆ V is called a total dominating set if every vertex of V is adjacent to some vertex of S. Interest in total domination began when the

Fundamentals of domination in graphs

Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of

A survey of selected recent results on total domination in graphs

Domination in graphs : advanced topics

LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizations