On some properties of characteristics polynomials of the complete Graphs Kn

Abstract EN

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.