The Gallai graph and therefore the anti-Gallai graph of a graph G have the perimeters of G as their vertices. 2 edges of G ar adjacent within the Gallai graph of G if they're incident however don't span a triangle in G; they're adjacent within the anti-Gallai graph of G if they span a triangle in G. during this paper we tend to show: The Four Color Theorem are often equivalently explicit in terms of anti-Gallai graphs; the issues of crucial the inner circle range, and therefore the chromatic range of a Gallai graph ar NP-complete. moreover, we tend to discuss the relation of Gallai graphs to the speculation of excellent graphs. A characterization of Gallai graphs and anti-Gallai graphs is additionally given .
Published Date: 2021-04-28; Received Date: 2021-04-02