Some results on the Laplacian spectrum

  • Authors:

  • Muhuo Liu;Bolian Liu

  • Affiliations:

  • Department of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, PR China and School of Mathematical Science, South China Normal University, Guangzhou, 510631, PR China;School of Mathematical Science, South China Normal University, Guangzhou, 510631, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

A graph is called a Laplacian integral graph if the spectrum of its Laplacian matrix consists of integers, and a graph G is said to be determined by its Laplacian spectrum if there does not exist other non-isomorphic graph H such that H and G share the same Laplacian spectrum. In this paper, we obtain a sharp upper bound for the algebraic connectivity of a graph, and identify all the Laplacian integral unicyclic, bicyclic graphs. Moreover, we show that all the Laplacian integral unicyclic, bicyclic graphs are determined by their Laplacian spectra.