da Fonseca, Carlos
|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Tridiagonal Matrices and Spectral Properties of Some Graph Classes||Journal:||Czechoslovak Mathematical Journal||Issue Date:||23-Apr-2020||Rank:||M23||ISSN:||0011-4642||DOI:||10.21136/CMJ.2020.0182-19||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. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval a chain graph does not have any nonzero eigenvalue. A similar result is provided for threshold graphs.
|Keywords:||05C50 | chain graph | eigenvalue-free interval | threshold graph | tridiagonal matrix||Publisher:||Institute of Mathematics of the Czech Academy of Sciences; Springer Link|
Show full item record
checked on Sep 16, 2022
checked on Sep 15, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.