doiSerbia

The signless Laplacian spectral radius of bounded degree graphs on surfaces

Yu Guihai (School of Mathematics, Shandong Institute of Business and Technology, Yantai, Shandong, China + Central South University, School of Mathematics and Statistics, New Campus, Changsha, Hunan, China)
Feng Lihua (School of Mathematics and Statistics, Central South University, New Campus, Changsha, Hunan, China,)
Ilić Aleksandar (Mathematical Institute, Serbian Academy of Science and Arts, Belgrade)
Stevanović Dragan (Mathematical Institute, Serbian Academy of Science and Arts, Belgrade + University of Primorska, Institute Andrej Marušić, Koper, Slovenia)

Let G be an n-vertex (n ≥ 3) simple graph embeddable on a surface of Euler genus (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: signless Laplacian matrix, spectral radius, Euler genus, outerplanar graph, Halin graph