Aparna Lakshmanan S., Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India, e-mail: firstname.lastname@example.org; S. B. Rao, Stat-Math Unit, Indian Statistical Institute, Kolkata-700 108, India, e-mail: email@example.com; A. Vijayakumar, Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India, e-mail: firstname.lastname@example.org
Abstract: 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.
Keywords: Gallai graphs, anti-Gallai graphs, cographs
Classification (MSC2000): 05C99
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