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Czechoslovak Mathematical Journal

, Volume 64, Issue 2, pp 311–325 | Cite as

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

  • Guoping Wang
  • Guangquan Guo
  • Li Min
Article

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.

Keywords

signless Laplacian spectrum cospectral graphs T-shape tree 

MSC 2010

05C50 15A18 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesXinjiang Normal University, UrumqiXinjiangP.R. China

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