The signless Laplacian spectral radius of bounded degree graphs on surfaces

Applicable Analysis and Discrete Mathematics

article

Guihai Yu¹  Lihua Feng²  Aleksandar Ilić³  Dragan Stevanović³ 

[1] School of Mathematics, Shandong Institute of Business and Technology;School of Mathematics and Statistics, Central South University, New Campus;Mathematical Institute, Serbian Academy of Science and Arts;University of Primorska, Institute Andrej Maruˇsiˇc

关键词: Signless Laplacian matrix;    spectral radius;    Euler genus;    outerplanar graph;    Halin graph.;   

DOI  :  10.2298/AADM150722015Y

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Let G be an n-vertex (n ≥ 3) simple graph embeddable on a surface of Eulergenus γ (the number of crosscaps plus twice the number of handles). In thispaper, we present upper bounds for the signless Laplacian spectral radius ofplanar graphs, outerplanar graphs and Halin graphs, respectively, in termsof order and maximum degree. We also demonstrate that our bounds aresometimes better than known ones. For outerplanar graphs without internaltriangles, we determine the extremal graphs with the maximum and minimumsignless Laplacian spectral radii.

【 授权许可】

Unknown