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Sharp lower bounds on the least eigenvalue of graphs determined from edge clique partitions
release_ts5nlxwsyfdshdfhlbti3a3do4
by
Domingos M. Cardoso and Inês Serôdio Costa and Rui Duarte
Released
as a article
.
2022
Abstract
A lower bound on the least eigenvalue of an arbitrary graph and a necessary
and sufficient condition for this lower bound to be attained are deduced using
an edge clique partition. As an application, we prove that the least eigenvalue
of the n-Queens' graph 𝒬(n) is equal to -4 for every n ≥ 4
and it is also proven that the multiplicity of this eigenvalue is (n-3)^2.
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2201.01224v2
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