Authors: | Anđelić, Milica Ghorbani, Ebrahim Simić, Slobodan |
Title: | Vertex types in threshold and chain graphs | Journal: | Discrete Applied Mathematics | Volume: | 269 | First page: | 159 | Last page: | 168 | Issue Date: | 30-Sep-2019 | Rank: | M22 | ISSN: | 0166-218X | DOI: | 10.1016/j.dam.2019.02.040 | Abstract: | A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. A threshold graph can be obtained from a chain graph by making adjacent all pairs of vertices in one colour class. Given a graph G, let λ be an eigenvalue (of the adjacency matrix) of G with multiplicity k≥1. A vertex v of G is a downer, or neutral, or Parter depending whether the multiplicity of λ in G−v is k−1, or k, or k+1, respectively. We consider vertex types in the above sense in threshold and chain graphs. In particular, we show that chain graphs can have neutral vertices, disproving a conjecture by Alazemi et al. |
Keywords: | Adjacency spectrum | Chain graphs | Threshold graphs | Vertex types | Publisher: | Elsevier | Project: | IPM, Grant No. 96050211 Graph theory and mathematical programming with applications in chemistry and computer science |
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