On the smallest eigenvalues of the line graphs of some trees
  In this paper, we study the characteristic polynomials of the line graphs of generalized Bethe trees. We give an infinite family of such graphs sharing the same smallest eigenvalue. Our family generalizes the family of coronas of complete graphs discovered by Cvetkovi\'c and Stevanovi\'c. 
Akihiro Munemasa, Yoshio Sano, and Tetsuji Taniguchi
math.CO cs.DM