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Sums of squares of eigenvalues and the vector chromatic number

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arxiv 2308.04475 v1 pith:TZPXCRTE submitted 2023-08-08 math.CO

Gabriel Coutinho , Thomás Jung Spier This is my paper · ORCID
classification math.CO
keywords chromaticeigenvaluesnumbersquaresvectoradjacencyaneksteinbounded
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In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided by the vector chromatic number, resolving a conjecture by Wocjan, Elphick and Anekstein (2018).

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  1. The positive and negative square-energy conjecture

    math.CO 2026-07 accept novelty 8.0 of 10

    Every connected graph G on n vertices satisfies min{s+(G), s−(G)} ≥ n−1, confirming the Elphick–Farber–Goldberg–Wocjan conjecture.

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