Hypoenergetic and strongly hypoenergetic trees

2009/05/25 by Xueliang Li, Li, Xueliang, Hongping Ma +1
Mathematics · #05C50 #05C90 #15A18 #92E10 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #math.CO #msc:05C50 #msc:05C90 #msc:15A18 #msc:92E10

paper · pdf · doi:10.48550/arxiv.0905.3944

8 pages

openalex publication_date 2009/05/25 · arxiv created 2009/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The energy E(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of G. An n-vertex graph is said to be hypoenergetic if E(G)<n and strongly hypoenergetic if E(G)<n-1. In this paper, we consider hypoenergetic and strongly hypoenergetic trees. For any given n and Δ, the existence of both hypoenergetic and strongly hypoenergetic trees of order n and maximum degree Δ is completely characterized.

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