Nordhaus-gaddum inequalities for anti fuzzy graph

Abstract

The objective of this paper is to finds the lower and upper bounds of Nordhaus-Gaddum inequalities of fuzzy chromatic number for anti-fuzzy graph. This paper analyzes the chromatic index of complementary anti fuzzy graphs in some cases. A theorem is proved for anti-fuzzy graph to be k-critical. Examples are provided to derive the vertex coloring of these graphs.