# Vertex types in threshold and chain graphs

@article{Andelic2019VertexTI, title={Vertex types in threshold and chain graphs}, author={Milica Andelic and Ebrahim Ghorbani and Slobodan K. Simic}, journal={Discret. Appl. Math.}, year={2019}, volume={269}, pages={159-168} }

A graph is called a chain graph if it is bipartite and the neighborhoods of the vertices in each color 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 color class. Given a graph $G$, let $\lambda$ be an eigenvalue (of the adjacency matrix) of $G$ with multiplicity $k \geq 1$. A vertex $v$ of $G$ is a downer, or neutral, or Parter depending whether the multiplicity of $\lambda$ in $G-v$ is $k-1…

## 3 Citations

Wiener Index of Chain Graphs

- 2020

A bipartite graph is called a chain graph if the neighborhoods of the vertices in each partite set form a chain with respect to set inclusion. Chain graphs are discovered and re-discovered by various…

Tridiagonal Matrices and Spectral Properties of Some Graph Classes

- Mathematics
- 2020

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. In this paper we give an explicit formula for…

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