Note for Nikiforov's two conjectures on the energy of trees

Details Note for Nikiforov's two conjectures on the energy of trees Note for Nikiforov's two conjectures on the energy of trees

2009-06-04

arxiv.org/abs/0906.0827v1

Mathematics

Combinatorics

5 pages

Scientific paper

The energy $E$ of a graph is defined to be the sum of the absolute values of
its eigenvalues. Nikiforov in {\it ``V. Nikiforov, The energy of $C_4$-free
graphs of bounded degree, Lin. Algebra Appl. 428(2008), 2569--2573"} proposed
two conjectures concerning the energy of trees with maximum degree $\Delta\leq
3$. In this short note, we show that both conjectures are true.

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