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

Authors: B. Praba; G. Deepa; V.M. Chandrasekaran

Addresses: SSN College of Engineering, Kalavakkam, Chennai, Tamilnadu, India ' School of Advanced Sciences, VIT University, Vellore-632014, Tamilnadu, India ' School of Advanced Sciences, VIT University, Vellore-632014, Tamilnadu, India

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.

Keywords: energy of a graph; energy of a fuzzy graph; energy of an intuitionistic fuzzy graph; Laplacian energy of a graph; Laplacian energy of a fuzzy graph.

DOI: 10.1504/IJASS.2018.096097

International Journal of Applied Systemic Studies, 2018 Vol.8 No.3, pp.196 - 217

Received: 11 Apr 2017
Accepted: 22 Feb 2018
Published online: 12 Nov 2018 *

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