Adjacency Sequence and Adjacency Spectrum of Power Fuzzy Graphs

Objectives: To find the adjacency sequence, spectrum of the power fuzzy graphs and discuss its properties. Methods: The spectrum and energy of the power fuzzy graphs are derived using the adjacency matrices. Energy of the power fuzzy graph is computed by adding the absolute eigenvalues of the adjacency matrix. Findings: The condition for a power fuzzy graph, 𝐺𝑓 𝑘 to be vertex regular in terms of adjacency sequence has been verified. The energy sequence for the power fuzzy graph with increasing 𝑘 has been established. Novelty: The concept of minimizing the interval of the edge membership values when the powers of fuzzy graph increase makes difference in the spectrum and energy of fuzzy graphs with the same initial structure. The concept of adjacency matrix, spectrum and energy of power fuzzy graph is applied in power supply load distribution system. Keywords: Fuzzy graph; Power fuzzy graph; Adjacency sequence; Spectrum; Energy