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

Guoping Wang; Guangquan Guo; Li Min

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 2, page 311-325
  • ISSN: 0011-4642

Abstract

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A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply G is D Q S ). 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 , 2 t + 1 ) ) ( t ≥ 1 ) are D Q S , and determine the graphs which have the same signless Laplacian spectrum as ℒ ( T ( t , t , 2 t + 1 ) ) . Let μ 1 ( G ) be the maximum signless Laplacian eigenvalue of the graph G . We give the limit of μ 1 ( ℒ ( T ( a , b , c ) ) ) , too.

How to cite

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Wang, Guoping, Guo, Guangquan, and Min, Li. "On the signless Laplacian spectral characterization of the line graphs of $T$-shape trees." Czechoslovak Mathematical Journal 64.2 (2014): 311-325. <http://eudml.org/doc/262019>.

@article{Wang2014,
abstract = {A graph is determined by its signless Laplacian spectrum if no other non-isomorphic 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 $\mathcal \{L\}(T(a,b,c))$ except $\mathcal \{L\}(T(t,t,2t+1))$ ($t\ge 1$) are $DQS$, and determine the graphs which have the same signless Laplacian spectrum as $\mathcal \{L\}(T(t,t,2t+1))$. Let $\mu _1(G)$ be the maximum signless Laplacian eigenvalue of the graph $G$. We give the limit of $\mu _1(\mathcal \{L\}(T(a,b,c)))$, too.},
author = {Wang, Guoping, Guo, Guangquan, Min, Li},
journal = {Czechoslovak Mathematical Journal},
keywords = {signless Laplacian spectrum; cospectral graphs; $T$-shape tree; signless Laplacian spectrum; cospectral graphs; -shape tree},
language = {eng},
number = {2},
pages = {311-325},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the signless Laplacian spectral characterization of the line graphs of $T$-shape trees},
url = {http://eudml.org/doc/262019},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Wang, Guoping
AU - Guo, Guangquan
AU - Min, Li
TI - On the signless Laplacian spectral characterization of the line graphs of $T$-shape trees
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 311
EP - 325
AB - A graph is determined by its signless Laplacian spectrum if no other non-isomorphic 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 $\mathcal {L}(T(a,b,c))$ except $\mathcal {L}(T(t,t,2t+1))$ ($t\ge 1$) are $DQS$, and determine the graphs which have the same signless Laplacian spectrum as $\mathcal {L}(T(t,t,2t+1))$. Let $\mu _1(G)$ be the maximum signless Laplacian eigenvalue of the graph $G$. We give the limit of $\mu _1(\mathcal {L}(T(a,b,c)))$, too.
LA - eng
KW - signless Laplacian spectrum; cospectral graphs; $T$-shape tree; signless Laplacian spectrum; cospectral graphs; -shape tree
UR - http://eudml.org/doc/262019
ER -

References

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