We characterize the eigenvalues and energy of the line graph L(G) whenever G is (i) a generalized Bethe tree, (ii) a Bethe tree, (iii) a tree defined by generalized Bethe trees attached to a path, (iv) a tree defined by generalized Bethe trees having a common root, (v) a graph defined by copies of a generalized Bethe tree attached to a cycle and (vi) a graph defined by copies of a star attached to a cycle; in this case, explicit formulas for the eigenvalues and energy of L(G) are derived. © 2010 Elsevier Inc. All rights reserved.
Rojo, O., & Jiménez, R. D. (2011). Line graph of combinations of generalized bethe trees: Eigenvalues and energy. Linear Algebra and Its Applications, 435(10), 2402–2419. https://doi.org/10.1016/j.laa.2010.10.008