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arXiv · 1208.5835

On the Main Signless Laplacian Eigenvalues of a Graph

Hanyuan Deng·He Huang
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Abstract

A signless Laplacian eigenvalue of a graph $G$ is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, we first give the necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless Laplacian eigenvalues, and then characterize the trees and unicyclic graphs with exactly two main signless Laplacian eigenvalues, respectively.

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Hanyuan Deng, He Huang. 2012-08-29. On the Main Signless Laplacian Eigenvalues of a Graph. https://arxiv.org/abs/1208.5835

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