Affiliations: Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, HP, India
Correspondence:
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Corresponding author. Rakesh Kumar Bajaj, Department of Mathematics, Jaypee University of Information
Technology, Waknaghat, Solan, Pin-173 234, HP, India. E-mail: rakesh.bajaj@gmail.com.
Abstract: In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternatives has been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.
Keywords: Picture fuzzy graph, score function, energy of graph, Laplacian energy, adjacency matrix, spectrum
