The graphs of pyramids are determined by their spectrum
arXiv (Cornell University)（2023）
Abstract
For natural numbers $k1$ we refer to $T_{n,k}$ as a \emph{graph of pyramids}. We prove that the graphs of pyramids are determined by their spectrum, and that a star $S_{n}$ is determined by its spectrum iff $n$ is prime. We also show that the graphs $T_{n,k}$ are completely positive iff $k\le2$.
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Key words
pyramids,graphs,spectrum
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