Boris Shapiro

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19962026

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math.CO2026

Transposition Cayley Spectra and Subgraph Counts

Boris Shapiro

Let $G$ be a finite simple graph on the vertex set $[n]$ , and let $Γ (G)$ be the Cayley graph of the symmetric group $S_{n}$ generated by the transpositions corresponding to the edges…

math.CO2026

The (n-2,2)-Spectrum of a Graph

Boris Shapiro

We study a representation-theoretic refinement of the ordinary Laplacian spectrum of a graph. Given a graph $G$ on $n$ vertices, one may associate to it the element \[ X_G=\sum_{ij…