✦ LIBER ✦

On a conjecture about the hypoenergetic trees

✍ Scribed by Jianping Liu; Bolian Liu

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 308 KB
Volume: 23
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.12.009

No coin nor oath required. For personal study only.

✦ Synopsis

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. An n-vertex graph G is said to be hypoenergetic if E(G) < n. In Gutman et al. (2008) [14] the authors conjectured that there exist n-vertex hypoenergetic trees with maximum degree ∆ = 4 for any n ≡ 2 mod 4, n > 2. In this paper we confirm this conjecture.

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