On the k-independence number of graphs

A. Abiad; G. Coutinho; M. A. Fiol

doi:10.1016/j.disc.2019.01.016

On the k-independence number of graphs

A. Abiad^*, G. Coutinho, M. A. Fiol

^*Corresponding author for this work

QE Operations research

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

This paper generalizes and unifies the existing spectral bounds on the k-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than k. The previous bounds known in the literature follow as a corollary of the main results in this work. We show that for most cases our bounds outperform the previous known bounds. Some infinite families of graphs where the bounds are tight are also presented. Finally, as a byproduct, we derive some spectral lower bounds for the diameter of a graph.

Original language	English
Pages (from-to)	2875-2885
Number of pages	11
Journal	Discrete Mathematics
Volume	342
Issue number	10
DOIs	https://doi.org/10.1016/j.disc.2019.01.016
Publication status	Published - Oct 2019
Event	Algebraic and Extremal Graph Theory Conference - University of Delaware, Newark, United States Duration: 7 Aug 2017 → 10 Aug 2017

Keywords

Graph
k-independence number
Spectrum
Interlacing
Regular partition
Antipodal distance-regular graph
CHROMATIC NUMBER
DISTANCE
POLYNOMIALS

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title = "On the k-independence number of graphs",

abstract = "This paper generalizes and unifies the existing spectral bounds on the k-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than k. The previous bounds known in the literature follow as a corollary of the main results in this work. We show that for most cases our bounds outperform the previous known bounds. Some infinite families of graphs where the bounds are tight are also presented. Finally, as a byproduct, we derive some spectral lower bounds for the diameter of a graph. ",

keywords = "Graph, k-independence number, Spectrum, Interlacing, Regular partition, Antipodal distance-regular graph, CHROMATIC NUMBER, DISTANCE, POLYNOMIALS",

author = "A. Abiad and G. Coutinho and Fiol, {M. A.}",

note = "data source: no data used; Algebraic and Extremal Graph Theory Conference ; Conference date: 07-08-2017 Through 10-08-2017",

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doi = "10.1016/j.disc.2019.01.016",

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T1 - On the k-independence number of graphs

AU - Abiad, A.

AU - Coutinho, G.

AU - Fiol, M. A.

N1 - data source: no data used

PY - 2019/10

Y1 - 2019/10

N2 - This paper generalizes and unifies the existing spectral bounds on the k-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than k. The previous bounds known in the literature follow as a corollary of the main results in this work. We show that for most cases our bounds outperform the previous known bounds. Some infinite families of graphs where the bounds are tight are also presented. Finally, as a byproduct, we derive some spectral lower bounds for the diameter of a graph.

AB - This paper generalizes and unifies the existing spectral bounds on the k-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than k. The previous bounds known in the literature follow as a corollary of the main results in this work. We show that for most cases our bounds outperform the previous known bounds. Some infinite families of graphs where the bounds are tight are also presented. Finally, as a byproduct, we derive some spectral lower bounds for the diameter of a graph.

KW - Graph

KW - k-independence number

KW - Spectrum

KW - Interlacing

KW - Regular partition

KW - Antipodal distance-regular graph

KW - CHROMATIC NUMBER

KW - DISTANCE

KW - POLYNOMIALS

U2 - 10.1016/j.disc.2019.01.016

DO - 10.1016/j.disc.2019.01.016

M3 - Article

SN - 0012-365X

VL - 342

SP - 2875

EP - 2885

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 10

T2 - Algebraic and Extremal Graph Theory Conference

Y2 - 7 August 2017 through 10 August 2017

ER -

On the k-independence number of graphs

Abstract

Keywords

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