Spectral radius of finite and infinite planar graphs and of graphs of bounded genus

Authors:
Zdenk Dvořák;Bojan Mohar
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada;Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada
Venue:
Journal of Combinatorial Theory Series B
Year:
2010

Citing 8
Cited 2

Some relations between analytic and geometric properties for infinite graphs

Discrete Mathematics
On the spectral radius and the genus of graphs

Journal of Combinatorial Theory Series B
The spectral radius of graphs on surfaces

Journal of Combinatorial Theory Series B
Tree amalgamation of graphs and tessellations of the Cantor sphere

Journal of Combinatorial Theory Series B
A simple condition implying rapid mixing of single-site dynamics on spin systems

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Some Recent Progress and Applications in Graph Minor Theory

Graphs and Combinatorics
Randomly coloring planar graphs with fewer colors than the maximum degree

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Covering planar graphs with forests, one having bounded maximum degree

Journal of Combinatorial Theory Series B

Spectrally degenerate graphs: Hereditary case

Journal of Combinatorial Theory Series B
A Framework for Coxeter Spectral Analysis of Edge-bipartite Graphs, their Rational Morsifications and Mesh Geometries of Root Orbits

Fundamenta Informaticae

Quantified Score

Hi-index	0.00

Visualization

Abstract

It is well known that the spectral radius of a tree whose maximum degree is @D cannot exceed 2@D-1. In this paper we derive similar bounds for arbitrary planar graphs and for graphs of bounded genus. Using the decomposition result of Goncalves (2009) [9], we prove that the spectral radius @r(G) of a planar graph G of maximum vertex degree @D=2 satisfies @r(G)=