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Given a symmetric matrix $M = [m_{ij}]$, or equivalently
a weighted graph ${\hat G}$ whose edge $ij$ has the
weight $m_{ij}$, let $\mu$ be its eigenvalue of multiplicity $k \geq
1$. Let $M_i$ be the principal submatrix of $M$ obtained by deleting
both $i$-th row and $i$-th column from $M$. Then $i$ is a {\em
downer}, or {\em neutral}, or {\em Parter} vertex of $M$ and/or
${\hat G}$, depending whether the multiplicity of $\mu$ in $M_i$ or
${\hat G}-i$ is $k-1$, or $k$, or $k+1$, respectively. We consider
vertex types in the sense of downer-, neutral- and Parter- vertices
in threshold and chain graphs.
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