Reflexive Line Graphs of Trees and Salem Numbers
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An elegant full characterization of reflexive line graphs of trees has proved to be quite difficult task. This paper tries to shed some more light on known results about such graphs by providing more numerical details regarding their structural composition. The paper also presents numerous results and ideas on the topic, as well as some observations with respect to the connection with Salem numbers.
KeywordsLine graph subdivision graph adjacency matrix second largest eigenvalue reflexive graph Salem graph
Mathematics Subject Classification15A18 05C50
- 5.Gumbrell, L.: On spectral constructions for Salem graphs, Doctoral Thesis, Royal Holloway, University of London (2013)Google Scholar
- 9.McKee, J.F., Rowlinson, P., Smyth, C.J.: Salem numbers and Pisot numbers from stars. In: Györy, K., Iwaniec, H., Urbanowicz, J. (eds.) Number Theory in Progress, vol. I, pp. 309–319. de Gruyter, Berlin (1999)Google Scholar
- 14.Radosavljević, Z., Simić, S.: Which bicyclic graphs are reflexive? Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat. 7, 90–104 (1996)Google Scholar