A Study of the Energy and Spectral Characteristics of the Knight’s Hypergraph
Santhosh Kumar N *
Department of Mathematics, Farook College, India and CKGM Govt. College, Perambra, India.
Suma P
PTM Govt. College, Perinthalmanna, India.
Jasmine Mathew
CKGM Govt. College, Perambra, India.
*Author to whom correspondence should be addressed.
Abstract
Hypergraphs are generalization of graphs, introduced by Berge. In an ordinary graph, an edge connects exactly two vertices, whereas in hypergraphs, a hyperedge can join any number of vertices. Hypergraphs have applications in the field of Computer Science, Machine learning, Neural networks etc . In this paper, we focus on the Knight’s hypergraph in which the squares of a chessboard are taken as vertices and each hyperedge include a vertex and all the vertices which are reachable by a knight in one move. We find the Adjacency matrix, Laplacian matrix, their eigenvalues and corresponding energies of the Knight’s hypergraph with the help of Python programming.
Keywords: Hypergraph, Adjacency matrix, Laplacian matrix, eigen spectrum, energy, knight’s hypergraph