On the multiplicity of distance signless Laplacian eigenvalues of graphs. Issue 11 (1st November 2020) - Xue, Jie
ABSTRACT: In this paper, we characterize all connected graphs, which have a distance signless Laplacian eigenvalue with multiplicity at least n − 2. As an application, we show that all these graphs, except K 2 ∨ 3 K 1 and K 1 ∨ ( K 3 + K 1 ), are determined by their distance signless Laplacian spectra. Moreover, we also determine all graphs with the third largest distance signless Laplacian eigenvalue equals n − 2.