Gallai and Anti-gallai Graphs of a Graph

@inproceedings{Lakshmanan2007GallaiAA,
  title={Gallai and Anti-gallai Graphs of a Graph},
  author={A. Ganesh Lakshmanan and Cochin and Siddani Bhaskara Rao},
  year={2007}
}
The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.