Lakshmanan,Aparna; Rao, S B; Vijayakumar,A(February 4, 2010)
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Abstract:
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.
this paper, the median and the antimedian of cographs are
discussed. It is shown that if G, and G2 are any two cographs, then there is a
cograph that is both Eulerian and Hamiltonian having Gl as its median and G2
as its antimedian. Moreover, the connected planar and outer planar cographs
are characterized and the median and antimedian graphs of connected, planar
cographs are listed.