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

Lower and upper bound of the Laplacian energy with real and complex roots of an intuitionistic... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Applied Systemic Studies Inderscience Publishers

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

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Publisher
Inderscience Publishers
Copyright
Copyright © Inderscience Enterprises Ltd
ISSN
1751-0589
eISSN
1751-0597
DOI
10.1504/IJASS.2018.096097
Publisher site
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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.

Journal

International Journal of Applied Systemic StudiesInderscience Publishers

Published: Jan 1, 2018

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