Authors: Yu, Guihai
Feng, Lihua
Ilić, Aleksandar
Stevanović, Dragan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The signless laplacian spectral radius of bounded degree graphs on surfaces
Journal: Applicable Analysis and Discrete Mathematics
Volume: 9
Issue: 2
First page: 332
Last page: 346
Issue Date: 1-Jan-2015
ISSN: 1452-8630
DOI: 10.2298/AADM150722015Y
Let G be an n-vertex (n ≥ 3) simple graph embeddable on a surface of Euler genus γ (the number of crosscaps plus twice the number of handles). In this paper, we present upper bounds for the signless Laplacian spectral radius of planar graphs, outerplanar graphs and Halin graphs, respectively, in terms of order and maximum degree. We also demonstrate that our bounds are sometimes better than known ones. For outerplanar graphs without internal triangles, we determine the extremal graphs with the maximum and minimum signless Laplacian spectral radii.
Keywords: Euler genus | Halin graph | Outerplanar graph | Signless Laplacian matrix | Spectral radius
Publisher: School of Electrical Engineering, University of Belgrade
Project: NSFC (Grants no. 11101245, 11271208,61202362, 11301302)
NSF of Shandong (No. BS2013SF009)
Graph theory and mathematical programming with applications in chemistry and computer science 
Slovenian Agency for Research, Project J1-4021

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