Proofs of a few special cases of a conjecture on energy of non-singular graphsi

Abstract

Akbari and Hosseinzadeh [MATCH Commun. Math. Comput. Chem. 83 (2020), 631{633] conjectured that the energy of a non-singular graph G is bounded from below by the sum of the maximum and the minimum vertex degree of G, with equality if and only if G is a complete graph. We discuss this conjecture here and provide a few lower bounds on the energy which prove this conjecture in several special cases.