Spectral properties of king’s graph
摘要
Spectra of a graph refer to the eigenvalues of the matrix associated with it. The graph energy is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix. In this paper, I obtain the spectra of the adjacency matrix and its properties, as well as the graph energy, for the King's graph with 1 row and n columns, 2 rows and n columns, 3 rows and n columns, m rows and n columns. This study is also extended to the square King's graph, which contains n rows and n columns.