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arXiv · 1304.3524

Characterization of tricyclic graphs with exactly two $Q$-main eigenvalues

Shuchao Li·Xue Yang
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Abstract

The signless Laplacian matrix of a graph $G$ is defined to be the sum of its adjacency matrix and degree diagonal matrix, and its eigenvalues are called $Q$-eigenvalues of $G$. A $Q$-eigenvalue of a graph $G$ is called a $Q$-main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Chen and Huang [L. Chen, Q.X. Huang, Trees, unicyclic graphs and bicyclic graphs with exactly two $Q$-main eigenvalues, submitted for publication] characterized all trees, unicylic graphs and bicyclic graphs with exactly two main $Q$-eigenvalues, respectively. As a continuance of it, in this paper, all tricyclic graphs with exactly two $Q$-main eigenvalues are characterized.

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Shuchao Li, Xue Yang. 2013-04-12. Characterization of tricyclic graphs with exactly two $Q$-main eigenvalues. https://arxiv.org/abs/1304.3524

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