27th Conference of the International Linear Algebra Society (ILAS 2026)

A graph energy conjecture through the lenses of semidefinite programming

May 19, 2026, 4:35 PM

25m

Goodwin Hall 125 (Virginia Tech)

Minisymposium Talk Spectral Graph Theory Spectral Graph Theory

Speaker

Emanuel Juliano (Federal University of Minas Gerais)

Description

In the 1980s, using the software Graffiti, Fajtlowicz made a conjecture relating the independence number of a graph with its energy, a spectral parameter introduced by Gutman (1978). By formulating the graph energy as a semidefinite program (SDP), we take a step towards Fajtlowicz's conjecture, relating the graph energy to the fractional clique covering number. As a byproduct of the SDP formulation, we obtain several lower bounds for the graph energy that improve and refine previous results by Hoffman (1970) and Nikiforov (2007).