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

2009/06/04 by Xueliang Li, Li, Xueliang, Jianxi Liu +1
Computer Science · Mathematics · Physics and Astronomy · #05C50 #05C90 #15A18 #92E10 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis #math.CO #msc:05C50 #msc:05C90 #msc:15A18 #msc:92E10

paper · pdf · doi:10.48550/arxiv.0906.0827

5 pages

arxiv created 2009/06/04 · openalex publication_date 2009/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C₄-free graphs of bounded degree, Lin. Algebra Appl. 428(2008), 2569--2573" proposed two conjectures concerning the energy of trees with maximum degree Δ≤ 3. In this short note, we show that both conjectures are true.

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