Title

The energy of C4-free graphs of bounded degree

Abstract

Answering some questions of Gutman, we show that, except for four specific trees, every connected graph G of order n, with no cycle of order 4 and with maximum degree at most 3, satisfies{divides} μ1 {divides} + ⋯ + {divides} μn {divides} ≥ n,where μ1, ..., μn are the eigenvalues of G. We give some general results and state two conjectures. © 2007 Elsevier Inc. All rights reserved.

Publication Title

Linear Algebra and Its Applications

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