Breakthrough Tracker record

A claimed proof of Fajtlowicz’s graph-energy conjecture

The paper claims a proof that the sum of the absolute adjacency eigenvalues of every graph is at least twice the difference between its order and independence number.

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Stable ID: math-fajtlowicz-energy-conjecture-2026
Revision: math-fajtlowicz-energy-conjecture-2026.v1
Field: Mathematics · Spectral graph theory
Evidence: Tier 1 · Peer reviewed: No
Record state: Provisional · Provisional claimed proof
Last checked: 2026-07-29

AI role

The authors disclose AI-tool use during ideation and state that the manuscript text was not AI-generated.

Record details

Problem or result: Whether every graph of order n satisfies energy at least 2(n minus its independence number)
Authors: Hitesh Kumar and Shivaramakrishna Pragada
Institutions: Simon Fraser University
Result date: Preprint submitted July 22, 2026

Why it matters

Fajtlowicz’s inequality has been an open spectral graph theory conjecture since the 1980s.

Limits

This is a first-version preprint without located independent specialist assessment or peer review. No formal proof artifact or independently rerun computation accompanies the claim.

Sources

Primary: Hitesh Kumar and Shivaramakrishna Pragada, Energy and independence number

Correction and revision history

2026-07-23 — Prepared as a provisional tracker addition; the universal quantifier, preprint status and limited disclosed AI role are retained.

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