On Determinant of Laplacian Matrix and Signless Laplacian Matrix of a Simple Graph

Abstract

In a simple graph, Laplacian matrix and signless Laplacian matrix are derived from both adjacency matrix and degree matrix. Although, determinant of Laplacian matrix is always zero, yet we express it using only the adjacency matrix and square of its adjacency matrix. Likewise, we express the determinant of signless Laplacian matrix using only the diagonal elements provided the signless Laplacian matrix is equal to the square of its adjacency matrix.