Laplacian energy of power fuzzy graphs with application in cryptography

The primary aim of this study is to present and expand on the idea of Laplacian energy within the context of power fuzzy graphs. The aim is to establish the Laplacian energy sequence for the power fuzzy graph with increasing power. The Laplacian spectrum and matrix are defined using the degree and adjacency matrices. The Laplacian energy of the power fuzzy graph is computed using eigenvalues of the corresponding Laplacian matrix and the size of the power fuzzy graph. The formal definition of the Laplacian matrix for power fuzzy graphs is defined, and the Laplacian energy sequence as power increases is computed. This concept is explored as a unique extension of fuzzy graphs and power graphs. Applying size, Laplacian matrix, and energy of regular power fuzzy graph theory to cryptography is a new method in this study.