Generation and properties of nut graphs
 Author
 Kris Coolsaet (UGent) , Patrick W Fowler and Jan Goedgebeur (UGent)
 Organization
 Project
 Abstract
 A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which nontrivial kernel vectors do not contain a zero. Chemical graphs arc connected, with maximum degree at most three. We present a new algorithm for the exhaustive generation of nonisomorphic nut graphs. Using this algorithm, we determined all nut graphs up to 13 vertices and all chemical nut graphs up to 22 vertices. Furthermore, we determined all nut graphs among the cubic polyhedra up to :14 vertices and all nut fullerenes up to 250 vertices. Nut graphs are of interest in chemistry of conjugated systems, in models of electronic structure, radical reactivity and molecular conduction. The relevant mathematical properties of chemical nut graphs are the position of the zero eigenvaluc in the graph spectrum, and the dispersion in magnitudes of kernel eigenvector entries (r: the ratio of maximum to minimum magnitude of entries). Statistics are gathered on these properties for all the nut graphs generated here. We also show that all chemical nut graphs have r >= 2 and that there is at least one chemical nut graph with r = 2 for every order n >= 9 (with the exception of n = 10).
 Keywords
 CHEMICAL GRAPHS, SINGULAR GRAPHS, FULLERENES, EIGENVALUES, ORBITALS, CORES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8591414
 MLA
 Coolsaet, Kris, et al. “Generation and Properties of Nut Graphs.” MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, vol. 80, no. 2, 2018, pp. 423–44.
 APA
 Coolsaet, K., Fowler, P. W., & Goedgebeur, J. (2018). Generation and properties of nut graphs. MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 80(2), 423–444.
 Chicago authordate
 Coolsaet, Kris, Patrick W Fowler, and Jan Goedgebeur. 2018. “Generation and Properties of Nut Graphs.” MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 80 (2): 423–44.
 Chicago authordate (all authors)
 Coolsaet, Kris, Patrick W Fowler, and Jan Goedgebeur. 2018. “Generation and Properties of Nut Graphs.” MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 80 (2): 423–444.
 Vancouver
 1.Coolsaet K, Fowler PW, Goedgebeur J. Generation and properties of nut graphs. MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY. 2018;80(2):423–44.
 IEEE
 [1]K. Coolsaet, P. W. Fowler, and J. Goedgebeur, “Generation and properties of nut graphs,” MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, vol. 80, no. 2, pp. 423–444, 2018.
@article{8591414, abstract = {{A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which nontrivial kernel vectors do not contain a zero. Chemical graphs arc connected, with maximum degree at most three. We present a new algorithm for the exhaustive generation of nonisomorphic nut graphs. Using this algorithm, we determined all nut graphs up to 13 vertices and all chemical nut graphs up to 22 vertices. Furthermore, we determined all nut graphs among the cubic polyhedra up to :14 vertices and all nut fullerenes up to 250 vertices. Nut graphs are of interest in chemistry of conjugated systems, in models of electronic structure, radical reactivity and molecular conduction. The relevant mathematical properties of chemical nut graphs are the position of the zero eigenvaluc in the graph spectrum, and the dispersion in magnitudes of kernel eigenvector entries (r: the ratio of maximum to minimum magnitude of entries). Statistics are gathered on these properties for all the nut graphs generated here. We also show that all chemical nut graphs have r >= 2 and that there is at least one chemical nut graph with r = 2 for every order n >= 9 (with the exception of n = 10).}}, author = {{Coolsaet, Kris and Fowler, Patrick W and Goedgebeur, Jan}}, issn = {{03406253}}, journal = {{MATCHCOMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY}}, keywords = {{CHEMICAL GRAPHS,SINGULAR GRAPHS,FULLERENES,EIGENVALUES,ORBITALS,CORES}}, language = {{eng}}, number = {{2}}, pages = {{423444}}, title = {{Generation and properties of nut graphs}}, volume = {{80}}, year = {{2018}}, }