Eigenvalue Bounds for the Signless Laplacian

Dragoš Cvetković; Peter Rowlinson; Slobodan Simić

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The distance Laplacian of a connected graph $G$ is defined by $ℒ = Diag (Tr) - 𝒟$ , 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 $ℒ$ is called the distance Laplacian spectrum of $G$ . In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties...