Q-integral graphs with edge–degrees at most five

We consider the problem of determining the Q-integral graphs, i.e. the graphs with integral signless Laplacian spectrum. We find all such graphs with maximum edge-degree 4, and obtain only partial results for the next natural case, with maximum edge-degree 5.

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Bibliographic Details
Published in:Discrete mathematics 2008-10, Vol.308 (20), p.4625-4634
Main Authors: SIMIC, Slobodan K, STANIC, Zoran
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Edge-degree
Exact sciences and technology
Information retrieval. Graph
Integral eigenvalues
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Signless Laplacian spectrum
Theoretical computing
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Description
Summary:We consider the problem of determining the Q-integral graphs, i.e. the graphs with integral signless Laplacian spectrum. We find all such graphs with maximum edge-degree 4, and obtain only partial results for the next natural case, with maximum edge-degree 5.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2007.08.055