This paper discusses the properties of the characteristic polynomial of the
complete graphs Kn, n=1, 2… respective to the adjacency matrices. Two different
types of matrices, the adjacency matrix and the signless Laplacian matrix, are
presented. A recurrence relation for computing the characteristic polynomials
depending on the adjacency matrix is introduced. We deduce that the coefficients of
the polynomials based on the two different matrices have a relationship with Pascal
triangle. The coefficients are computed using Matlab program. Many other properties
of these coefficients are discussed also.
Keywords: Laplacian matrix, Pascal triangle, Complete graph.
