# 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

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topWang, 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 -

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