Authors: Pokorný, Milan
Híc, Pavel
Stevanović, Dragan 
Milošević, Marko
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On distance integral graphs
Journal: Discrete Mathematics
Volume: 338
Issue: 10
First page: 1784
Last page: 1792
Issue Date: 31-May-2015
Rank: M22
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.03.004
The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D, and they form the distance spectrum of G. A graph is called distance integral if its distance spectrum consists entirely of integers. We show that no nontrivial tree can be distance integral. We characterize distance integral graphs in the classes of graphs similar to complete split graphs, which, together with relations between graph operations and distance spectra, allows us to exhibit many infinite families of distance integral graphs.
Keywords: Complete Split Graph | Distance integral graph | Distance spectrum | Tree
Publisher: Elsevier
Project: Graph theory and mathematical programming with applications in chemistry and computer science 
Slovenian Agency for Research program P1-0285 and the research projects J1-5433, J1-6720, J1-6743, and J7-6828
Slovak–Serbian bilateral project 680-00-140/2012-09/15
Slovak Ministry of Education, Grant No.1/0042/14

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