Open AccessLocating eigenvalues of unicyclic graphs
Author(s) -
O Rodrigo Braga,
MARCELA RODRIGUES,
Vilmar Trevisan
Publication year - 2017
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm1702273b
Subject(s) - mathematics , eigenvalues and eigenvectors , integral graph , combinatorics , graph , discrete mathematics , indifference graph , spectrum (functional analysis) , interval (graph theory) , line graph , voltage graph , physics , quantum mechanics
We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval. It operates directly on the graph, so that the matrix is not needed explicitly. The algorithm is applied to study the multiplicities of eigenvalues of closed caterpillars, obtain the spectrum of balanced closed caterpillars and give sufficient conditions for these graphs to be non-integral. We also use our method to study the distribution of eigenvalues of unicyclic graphs formed by adding a fixed number of copies of a path to each node in a cycle. We show that they are not integral graphs.