Signless Laplacian spectral characterization of line graphs of T-shape trees |
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Authors: | JianFeng Wang QiangLong Zhang |
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Affiliation: | Department of Mathematics, QingHai Normal University, XiNing, P.R. China. |
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Abstract: | A T-shape tree is a tree with exactly one vertex of maximum degree 3. The line graphs of the T-shape trees are triangles with a hanging path at each vertex. Let Ca,b,c be such a graph, where a, b and c are the lengths of the paths. In this paper, we show that line graphs of T-shape trees, with the sole exception of Ca,a,2a+1, are determined by the spectra of their signless Laplacian matrices. For the graph Ca,a,2a+1 we identify the unique non-isomorphic graph sharing the same signless Laplacian characteristic polynomial. |
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Keywords: | signless Laplacian spectral characterization line graph Q-matrix T-shape tree |
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