Some spectral properties of chain graphs
Combinatorics
2017-03-13 v1
Abstract
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. Alazemi, Andeli\'c and Simi\'c conjectured that no chain graph shares a non-zero (adjacency) eigenvalue with its vertex-deleted subgraphs. We disprove this conjecture. However, we show that the assertion holds for subgraphs obtained by deleting vertices of maximum degrees in either of color classes. We also give a simple proof for the fact that chain graphs have no eigenvalue in the interval .
Keywords
Cite
@article{arxiv.1703.03581,
title = {Some spectral properties of chain graphs},
author = {Ebrahim Ghorbani},
journal= {arXiv preprint arXiv:1703.03581},
year = {2017}
}