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arXiv · 2607.19817

Energy and independence number

Hitesh Kumar·Shivaramakrishna Pragada
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Abstract

For a graph $G$ of order $n$, with adjacency eigenvalues $λ_1(G) \geq \cdots \geq λ_n(G)$, the \emph{energy} of $G$ is defined to be \[\mathcal{E}(G)=\sum_{i=1}^{n} |λ_i(G)|.\] A well-known conjecture from the 1980s by Fajtlowicz states that for any graph $G$, \[\mathcal{E}(G) \ge 2\left(n-α(G)\right),\] where $α(G)$ denotes the independence number. We prove this conjecture.

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Hitesh Kumar, Shivaramakrishna Pragada. 2026-07-22. Energy and independence number. https://arxiv.org/abs/2607.19817

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