Some results on the Laplacian spectrum
A graph is called a Laplacian integral graph if the spectrum of its Laplacian matrix consists of integers, and a graph G G is said to be determined by its Laplacian spectrum if there does not exist other non-isomorphic graph H H such that H H and G 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.
laplacian spectrum laplacian matrix algebraic connectivity