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

Title:

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

Creator:

Wang, Guoping, Guo, Guangquan, and Li, Min

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8588f068-92e0-48fe-8b76-7bd9f432da74
uuid:8588f068-92e0-48fe-8b76-7bd9f432da74

Subject:

signless Laplacian spectrum, cospectral graphs, and $T$-shape tree

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $\mathcal {L}(T(t,t,2t+1))$ ($t\geq 1$) 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

311-325

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:2

Harvested from:

CDK

Metadata only:

false