On the characteristic polynomial of Laplacian Matrices of Caterpillars

TL;DR

This paper derives recursive formulas for the characteristic polynomials of Laplacian matrices of caterpillars and uses these results to establish bounds on their algebraic connectivity.

Contribution

It introduces recursive formulas for the characteristic polynomials of Laplacian matrices of caterpillars and applies them to bound algebraic connectivity.

Findings

Recursive formulas for characteristic polynomials of Laplacian matrices

Bounds on algebraic connectivity of caterpillars

Application to line graphs of caterpillars

Abstract

The characteristic polynomials of the adjacency matrix of line graphs of caterpillars and then the characteristic polynomials of their Laplacian or signless Laplacian matrices are characterized, using recursive formulas. Furthermore, the obtained results are applied on the determination of upper and lower bounds on the algebraic connectivity of these graphs.