A proof of the conjecture on hypoenergetic graphs with maximum degree Δ≤ 3

2009/06/15 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.0906.2604

10 pages

openalex publication_date 2009/06/15 · arxiv created 2009/06/16 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · 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 its eigenvalues. A graph G of order n is said to be hypoenergetic if E(G)<n. Majstorović et al. conjectured that complete bipartite graph K_2,3 is the only hypoenergetic connected quadrangle-containing graph with maximum degree Δ≤ 3. This paper is devoted to giving a confirmative proof to the conjecture.

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