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Spectral radius and clique partitions of graphs

Zhou,Jiang
; 
van Dam,Edwin R.
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.
Description
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.
Date
2021-12
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Tilburg University Research Output Collection
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Keywords
Clique partition, Clique partition number, Spectral radius, Steiner 2-design
Citation
Zhou, J & van Dam, E R 2021, 'Spectral radius and clique partitions of graphs', Linear Algebra and its Applications, vol. 630, pp. 84-94. https://doi.org/10.1016/j.laa.2021.07.025
URI
https://hdl.handle.net/20.500.14602/75775
License
info:eu-repo/semantics/closedAccess
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