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ELA

ON MINIMAL ENERGIES OF TREES WITH GIVEN DIAMETER

∗

SHUCHAO LI† AND NANA LI†

Abstract. The energy of G, denoted byE(G), is defined as the sum of the absolute values of the eigenvalues ofG. In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a conjecture proposed by B. Zhou and F. Li [J. Math. Chem., 39:465–473, 2006] is completely solved.

Key words. Energy, Tree, Pendent vertex, Diameter.

AMS subject classifications.05C50, 05C35.

∗Received by the editors January 7, 2008. Accepted for publication August 17, 2008. Handling

Editor: Stephen J. Kirkland.

†Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R.

China (lscmath@mail.ccnu.edu.cn, Shuchao Li). The research was partially supported by National Science Foundation of China (Grant No. 10671081).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 17, pp. 414-425, August 2008

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