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On the signless Laplacian spectral characterization of the line graphs of T-shape trees

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Abstract

A graph is determined by its signless Laplacian spectrum if no other nonisomorphic graph has the same signless Laplacian spectrum (simply G is DQS). Let T (a, b, c) denote the T-shape tree obtained by identifying the end vertices of three paths P a+2, P b+2 and P c+2. We prove that its all line graphs L(T(a, b, c)) except L(T(t, t, 2t+1)) (t ⩾ 1) are DQS, and determine the graphs which have the same signless Laplacian spectrum as L(T(t, t, 2t + 1)). Let µ1(G) be the maximum signless Laplacian eigenvalue of the graph G. We give the limit of µ1(L(T(a, b, c))), too.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P.R. China

    Guoping Wang, Guangquan Guo & Li Min

Authors
  1. Guoping Wang
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  2. Guangquan Guo
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  3. Li Min
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Correspondence to Guoping Wang.

Additional information

This work is supported by NSFC Grants No. 11261059 and No. 11461071.

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Wang, G., Guo, G. & Min, L. On the signless Laplacian spectral characterization of the line graphs of T-shape trees. Czech Math J 64, 311–325 (2014). https://doi.org/10.1007/s10587-014-0103-z

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  • DOI: https://doi.org/10.1007/s10587-014-0103-z

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