“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 15539 |
|
| Abstract: | |
|
Given a symmetric matrix M = [mij], or equivalently
a weighted graph ∧G whose edge ij has the
weight mij, let μ be its eigenvalue of multiplicity k ≥ 1. Let Mi be the principal submatrix of M obtained by deleting
both i-th row and i-th column from M. Then i is a
downer, or neutral, or Parter vertex of M and/or
∧G, depending whether the multiplicity of μ in Mi or
∧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.
Download TeX format |
|
| back to top | |
