English

Bounds on graph eigenvalues I

Combinatorics 2007-05-23 v3
Authors: Vladimir Nikiforov
View on arXiv ↗ PDF ↗

Abstract

We improve recent results relating graph eigenvalues to other graph parameters like girth, domination number, and minimum degree.

Keywords

graph laplacian graph theory spectral graph theory

Cite

@article{arxiv.math/0602027,
  title  = {Bounds on graph eigenvalues I},
  author = {Vladimir Nikiforov},
  journal= {arXiv preprint arXiv:math/0602027},
  year   = {2007}
}

Comments

Lihua Feng drew my attention to some shortcomings in the first version of the paper. General tightening and corrections

Related papers

View all related →
Combinatorics · Mathematics
New bounds on domination and independence in graphs
Jochen Harant, Samuel Mohr
2022-01-25
Combinatorics · Mathematics
Eigenvalues and extremal degrees in graphs
Vladimir Nikiforov
2007-05-23
Combinatorics · Mathematics
New bounds on the signed domination numbers of graphs
S. M. Hosseini Moghaddam, Abdollah Khodkar, Babak Samadi
2019-08-27
Combinatorics · Mathematics
More spectral bounds on the clique and independence numbers
Vladimir Nikiforov
2017-01-31
Combinatorics · Mathematics
Upper bounds for domination related parameters in graphs on surfaces
Vladimir Samodivkin
2013-10-08
Combinatorics · Mathematics
$(k,k',k'')$-domination in graphs
Abdollah Khodkar, Babak Samadi, H. R. Golmohammadi
2019-08-27
Combinatorics · Mathematics
Recent progress on graphs with fixed smallest eigenvalue
Jack H. Koolen, Meng-Yue Cao, Qianqian Yang
2020-11-25
Combinatorics · Mathematics
New lower bounds for the Geometric-Arithmetic index
Alvaro Martínez-Pérez, José M. Rodríguez
2017-03-17
Combinatorics · Mathematics
Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
Aida Abiad, Shaun M. Fallat, Mark Kempton, Rupert H. Levene +4
2023-09-01
Combinatorics · Mathematics
Bounds on higher graph gonality
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre, Cassandra Marcussen +4
2022-06-15
Combinatorics · Mathematics
Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph
Beth Bjorkman, Leslie Hogben, Scarlitte Ponce, Carolyn Reinhart +1
2018-11-19
Spectral Theory · Mathematics
An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs
A. Abiad, M. A. Fiol, W. H. Haemers, G. Perarnau
2013-11-20
Combinatorics · Mathematics
Combinatorial upper bounds for the smallest eigenvalue of a graph
Aryan Esmailpour, Sara Saeedi Madani, Dariush Kiani
2024-04-16
Combinatorics · Mathematics
Eigenvalues and degree deviation in graphs
Vladimir Nikiforov
2007-05-23
Combinatorics · Mathematics
On the surface area of graphs, related connectivity measures and spectral estimates
Patrizio Bifulco, Joachim Kerner
2026-03-09
Combinatorics · Mathematics
Asymptotic bounds on total domination in regular graphs
Carlos Hoppen, Giovane Mansan
2020-01-07
Combinatorics · Mathematics
Spectral Radius and maximum degree of connected graphs
Vladimir Nikiforov
2007-05-23
Combinatorics · Mathematics
Ends and vertices of small degree in infinite minimally k-(edge)-connected graphs
Maya Stein
2015-03-18
Discrete Mathematics · Computer Science
Lower Bounds for the Domination Numbers of Connected Graphs without Short Cycles
Yinglei Song
2016-01-05
Combinatorics · Mathematics
A few properties of the eigenvalues of normalized graph Laplacian
Anirban Banerjee
2014-03-07
Combinatorics · Mathematics
The edge-isoperimetric number of graphs and their powers: approaches from spectral graph theory, optimization and finite geometry
Aida Abiad, Nils van de Berg, Emanuel Juliano, Harper Reijnders +3
2026-01-27
Combinatorics · Mathematics
Eigenvalue bounds for some classes of matrices associated with graphs
Ranjit Mehatari, M. Rajesh Kannan
2020-08-27
Combinatorics · Mathematics
Eigenvalues of graphs and spectral Moore theorems
Sebastian M. Cioabă
2020-04-21
Combinatorics · Mathematics
Note on Nordhaus-Gaddum problems for power domination
Katherine F. Benson, Daniela Ferrero, Mary Flagg, Veronika Furst +2
2016-10-12
Combinatorics · Mathematics
Upper bound for the Laplacian eigenvalues of a graph
Miriam Farber, Ido Kaminer
2011-06-07