Symmetric Pascal matrices and related graphs

The symmetric Pascal matrix is a square matrix whose entries are given by binomial coefficients modulo 2. In 1997, Christopher and Kennedy defined and studied the binomial graph, which is the graph whose adjacency matrix is the symmetric Pascal matrix. They computed the spectrum of the binomial graph of order a power of 2. In this paper, we study spectral properties of the binomial graph of any order such as eigenvalues and eigenvectors, algebraic connectivities and inertia indices. We also compute the determinant of the symmetric Pascal matrix in modulo 3.