An antiregular graph is a simple graph with the maximum number of vertices with different degrees. In this paper we study the characteristic polynomial, the admittance (or Laplacian) polynomial and the matching polynomial of a connected antiregular graph. For these polynomials we obtain recurrences and explicit formulas. We also obtain some spectral properties. In particular, we prove an interlacing property for the eigenvalues and we give some bounds for the energy.

Characteristic, admittance and matching polynomials of an antiregular graph

MUNARINI, EMANUELE
2009

Abstract

An antiregular graph is a simple graph with the maximum number of vertices with different degrees. In this paper we study the characteristic polynomial, the admittance (or Laplacian) polynomial and the matching polynomial of a connected antiregular graph. For these polynomials we obtain recurrences and explicit formulas. We also obtain some spectral properties. In particular, we prove an interlacing property for the eigenvalues and we give some bounds for the energy.
Antiregual graphs; Maximally nonregular graphs; graph eigenvalues; graph energy; Chebyshev polynomials; Stirling numbers.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/561585
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