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G-2014-69

On the distance signless Laplacian of a graph

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The distance signless Laplacian of a connected graph G is defined by DQ=Diag(Tr)+D, where D is the distance matrix of G, and Diag(Tr) is the diagonal matrix whose main entries are the vertex transmissions in G. The spectrum of DQ is called the distance signless Laplacian spectrum of G. In the present paper, we study some properties of the distance signless Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance signless Laplacian eigenvalues. We prove several bounds on DQ eigenvalues and establish a relationship between n2 being a distance signless Laplacian eigenvalue of G and ¯G containing a bipartite component.

, 12 pages

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Linear and Multilinear Algebra , 64(6), 1113–1123, 2016 BibTeX reference

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