Spectral radius and clique partitions of graphs

Jiang Zhou; Edwin R. van Dam

doi:10.1016/j.laa.2021.07.025

Spectral radius and clique partitions of graphs

Jiang Zhou^*
, Edwin R. van Dam

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We give lower bounds on the size and total size of clique partitions of a graph in terms of its spectral radius and minimum degree, and derive a spectral upper bound for the maximum number of edge-disjoint t-cliques. The extremal graphs attaining the bounds are exactly the block graphs of Steiner 2-designs and the regular graphs with K_t-decompositions, respectively.

Original language	English
Pages (from-to)	84-94
Journal	Linear Algebra and its Applications
Volume	630
DOIs	https://doi.org/10.1016/j.laa.2021.07.025
Publication status	Published - Dec 2021

Keywords

Clique partition
Clique partition number
Spectral radius
Steiner 2-design

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10.1016/j.laa.2021.07.025

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abstract = "We give lower bounds on the size and total size of clique partitions of a graph in terms of its spectral radius and minimum degree, and derive a spectral upper bound for the maximum number of edge-disjoint t-cliques. The extremal graphs attaining the bounds are exactly the block graphs of Steiner 2-designs and the regular graphs with Kt-decompositions, respectively.",

keywords = "Clique partition, Clique partition number, Spectral radius, Steiner 2-design",

author = "Jiang Zhou and \{van Dam\}, \{Edwin R.\}",

note = "Funding Information: The authors would like to thank the reviewers for giving valuable suggestions. This work is supported by the National Natural Science Foundation of China (No. 11801115 and No. 12071097 ) and the Fundamental Research Funds for the Central Universities . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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AU - Zhou, Jiang

AU - van Dam, Edwin R.

N1 - Funding Information: The authors would like to thank the reviewers for giving valuable suggestions. This work is supported by the National Natural Science Foundation of China (No. 11801115 and No. 12071097 ) and the Fundamental Research Funds for the Central Universities . Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/12

Y1 - 2021/12

N2 - We give lower bounds on the size and total size of clique partitions of a graph in terms of its spectral radius and minimum degree, and derive a spectral upper bound for the maximum number of edge-disjoint t-cliques. The extremal graphs attaining the bounds are exactly the block graphs of Steiner 2-designs and the regular graphs with Kt-decompositions, respectively.

AB - We give lower bounds on the size and total size of clique partitions of a graph in terms of its spectral radius and minimum degree, and derive a spectral upper bound for the maximum number of edge-disjoint t-cliques. The extremal graphs attaining the bounds are exactly the block graphs of Steiner 2-designs and the regular graphs with Kt-decompositions, respectively.

KW - Clique partition

KW - Clique partition number

KW - Spectral radius

KW - Steiner 2-design

U2 - 10.1016/j.laa.2021.07.025

DO - 10.1016/j.laa.2021.07.025

M3 - Article

AN - SCOPUS:85112463604

SN - 0024-3795

VL - 630

SP - 84

EP - 94

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Spectral radius and clique partitions of graphs

Abstract

Keywords

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