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arXiv · 2111.02734

Spectral radius and clique partitions of graphs

Jiang Zhou·Edwin R. van Dam
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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 $K_t$-decompositions, respectively.

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Jiang Zhou, Edwin R. van Dam. 2021-11-04. Spectral radius and clique partitions of graphs. https://doi.org/10.1016/j.laa.2021.07.025

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