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arXiv · 2608.04367

Extremal Graphs for the Energy-Independence Number Inequality

Seyed Ahmad Mojallal
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Abstract

For a graph $G$ of order $n$, let $\mathcal E(G)$ denote its adjacency energy and let $\alpha(G)$ denote its independence number. A recent theorem of Kumar and Pragada states that $$\mathcal E(G)\ge 2\bigl(n-\alpha(G)\bigr).$$ We determine all graphs attaining equality. More precisely, equality holds if and only if every connected component of $G$ is an isolated vertex, a balanced complete multipartite graph, or a graph obtained by taking the disjoint union of $K_{a,\ldots,a}$ and $K_{b,\ldots,b}$, with the same number $r\ge3$ of parts, and then completely joining corresponding parts.

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Seyed Ahmad Mojallal. 2026-08-05. Extremal Graphs for the Energy-Independence Number Inequality. https://arxiv.org/abs/2608.04367

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