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The energy $E$ of a graph is defined to be the sum of the absolute values ofits eigenvalues. Nikiforov in {\it ``V. Nikiforov, The energy of $C_4$-freegraphs of bounded degree, Lin. Algebra Appl. 428(2008), 2569--2573"} proposedtwo conjectures concerning the energy of trees with maximum degree $\Delta\leq3$. In this short note, we show that both conjectures are true.

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