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Paper   IPM / M / 15539
School of Mathematics
  Title:   Vertex types in threshold and chain graphs
  Author(s):  Ebrahim Ghorbani (Joint with M. Andelic and S. K. Simic)
  Status:   Published
  Journal: Discrete Appl. Math.
  Vol.:  269
  Year:  2019
  Pages:   159-168
  Supported by:  IPM
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 Gi 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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