Geodesic
Gallai and anti-Gallai graphs of a graph
Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 43-54.

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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.
DOI : 10.21136/MB.2007.133996
Classification : 05C15, 05C75, 05C99
Keywords: Gallai graphs; anti-Gallai graphs; cographs 
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Lakshmanan S., Aparna; Rao, S. B.; Vijayakumar, A. Gallai and anti-Gallai graphs of a graph. Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 43-54. doi : 10.21136/MB.2007.133996. http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.133996/

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