The swap graph of the finite soluble groups |
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| Authors: | Marco Di Summa Andrea Lucchini |
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| Institution: | 1.State University of Novi Pazar,Novi Pazar,Serbia;2.Mathematical Institute SANU,Belgrade,Serbia;3.Faculty of Informatics and Computing,Singidunum University,Belgrade,Serbia;4.Department of Mathematics,Kuwait University,Safat,Kuwait |
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| Abstract: | A graph is reflexive if the second largest eigenvalue of its adjacency matrix is less than or equal to 2. In this paper, we characterize trees whose line graphs are reflexive. It turns out that these trees can be of arbitrary order—they can have either a unique vertex of arbitrary degree or pendant paths of arbitrary lengths, or both. Since the reflexive line graphs are Salem graphs, we also relate some of our results to the Salem (graph) numbers. |
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