On the multiplicity of distance signless Laplacian eigenvalues of graphs. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Xue, Jie; Liu, Shuting; Shu, Jinlong
• Is Part Of: Linear & multilinear algebra. Volume 68:Issue 11(2020)
• Page Start: 2276
• Page End: 2288
• Publication Date: 2020-11-01
• Subjects: J. Y. Shao; Multiplicity -- cospectrality -- distance signless Laplacian matrix; 05C50; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1578726
• Languages: English
• ISSNs: 0308-1087

Abstract

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.