Sums of squares of eigenvalues and the vector chromatic number

2023/08/08 by Gabriel Coutinho, Coutinho, Gabriel, Thomás Jung Spier +1
Mathematics · Engineering · Computer Science · #Graph theory and applications #graph theory and CDMA systems #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2308.04475

Abstract

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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