Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/1765
Title: There are exactly 172 connected Q-integral graphs up to 10 vertices
Authors: Stanić, Zoran 
Affiliations: Numerical Mathematics and Optimization 
Keywords: Signless Laplacian spectrum;Integral eigenvalues
Issue Date: 2007
Rank: M51
Publisher: Novi Sad : Department of Mathematics and Informatics, Faculty of Science
Journal: Novi Sad Journal of Mathematics
Abstract: 
A graph is called $Q$-integral if its signless Laplacian spectrum consists entirely of integers. We establish that there are exactly 172 connected $Q$-integral graphs up to 10 vertices. Pictures or adjacency matrices of those graphs, their $Q$-spectra, some data and comments are given. In addition, we present the connected graphs of the smallest order (which are neither regular nor complete bipartite) being integral in the sense of each of the following three spectra: usual one (related to the adjacency matrix), Laplacian and signless Laplacian.
URI: https://research.matf.bg.ac.rs/handle/123456789/1765
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