Spectral Properties and Energy Analysis of the Bishop Hypergraph on the 8×8 Chessboard
Abstract
In this paper, we investigate the Bishop hypergraph HB obtained from an 8×8 chessboard, where each square is treated as a vertex and two vertices are adjacent if a Bishop can move between them in a single move. We construct the adjacency and Laplacian matrices of the Bishop hypergraph HB and analyze their spectral properties. The eigenvalues of these matrices are computed numerically using Python, and the corresponding graph energies are evaluated. The results highlight the influence of diagonal-based connectivity on the spectrum and energy of the Bishop hypergraph HB and provide a comparative perspective with other chessboard based graphs.
Fields of Study & Subjects
Graph theory and applications
Graph Theory and Algorithms
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Journal of Advances in Mathematics and Computer Science
- Volume
- 41
- Issue
- 3
- Pages
- 126–141
- Publication date
- 11 March 2026
- Language
- EN