Lower and upper bound of the Laplacian energy with real and complex roots of an intuitionistic fuzzy directed graph

Abstract

In this paper, the concept of Laplacian energy of a fuzzy graph is extended to the Laplacian energy of an intuitionistic fuzzy directed graph. The degree matrix and the Laplacian energy of an intuitionistic fuzzy directed graph are defined. The upper and lower bound are derived for the Laplacian energy of an intuitionistic fuzzy directed graph. Existing work has been conjectured that the inequality E(G) ≤ LE(G) holds for all graphs. But we are conjectured that the inequality E(G) ≤ LE(G) does not hold for an intuitionistic fuzzy directed graph. Finally, numerical examples are illustrated for the defined work. Moreover, we analysed the results for the energy of an intuitionistic fuzzy directed graph and Laplacian energy of an intuitionistic fuzzy directed graph.