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Gallai and anti-Gallai graphs of a graph

S. Aparna LakshmananS. B. RaoA. Vijayakumar — 2007

Mathematica Bohemica

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.

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