arXiv:1405.3475 Abstract | arXiv Analytics

arXiv:1405.3475 [math.CO]Abstract References Reviews Resources

On the smallest eigenvalues of the line graphs of some trees

Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Published 2014-05-14, updated 2014-10-21Version 2

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.

Comments: 12 pages

Categories: math.CO, cs.DM

Subjects: 05C05, 05C50, 05C76

Keywords: line graphs, smallest eigenvalue, complete graphs, characteristic polynomials

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