• Corpus ID: 40269119

A Characterization of Connected (1,2)-Domination Graphs of Tournaments

@article{Factor2011ACO,
  title={A Characterization of Connected (1,2)-Domination Graphs of Tournaments},
  author={Kim A. S. Factor and Larry J. Langley},
  journal={AKCE International Journal of Graphs and Combinatorics},
  year={2011}
}
Recently, Hedetniemi et al. introduced (1, 2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1, 2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1, 2)-dominating graph of D, dom1,2 (D) , is defined to be the graph G = (V, E) , where V (G) = V (D) , and xy is an edge of G whenever x and y form a… 

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References

SHOWING 1-10 OF 12 REFERENCES

Domination Graphs of Tournaments and Digraphs

The domination graph of a digraph has the same vertices as the digraph with an edge between two vertices if every other vertex loses to at least one of the two. Previously, the authors showed that

The domination and competition graphs of a tournament

TLDR
It is shown dom(T) is either an odd cycle with possible pendant vertices or a forest of caterpillars, the complement of the competition graph of the tournament formed by reversing the arcs of T.

Domination Graphs with Nontrivial Components

TLDR
Which graphs containing no isolated vertices are domination graphs of tournaments are determined in this paper.

Secondary domination in graphs

Given a dominating set S ⊆ V in a graph G =( V,E), place one guard at each vertex in S. Should there be a problem at a vertex v ∈ V − S, we can send a guard at a vertex u ∈ S adjacent to v to handle

Secondary and Internal Distances of Sets in Graphs

For any given type of a set of vertices in a connected graph G =( V,E), we seek to determine the smallest integers (x,y : z) such that all minimal (or maximal) sets S of the given type, where |V | >

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

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

I. INTRODUCTION 1

The contributions in this book cast a spotlight into dark, often neglected, corners of the “information society” as articulated in the World Summit on the Information Society (WSIS). Several very

An Introduction to the Bootstrap

Statistics is the science of learning from experience, especially experience that arrives a little bit at a time. The earliest information science was statistics, originating in about 1650. This

Tournaments which yield connected domination graphs

  • Congr. Numer., 131
  • 1998