Cubic directed graphs with application

The purpose of this article is to present the Laplacian energy of cubic graphs and cubic directed graphs by analyzing the eigenvalues of the adjacency matrix and the Laplacian matrix. The proposed energy concept is discussed through mathematical and graphical models. Some useful properties related to cubic graph energies are studied, including their upper and lower bounds. The cubic fuzzy preference relationship is defined, and a multi-criteria decision-making model using the cubic fuzzy preference relationship is designed to select the best IT company for investment based on the energy of the cubic graph. Furthermore, an algorithm for solving the decision problem is described and the structure of the strategy is illustrated.