AI 中文总结
针对图论中邻接能量与独立数的不等式，本文确定了所有使等号成立的极值图结构。
AI 中文摘要
对于阶数为$n$的图$G$，令$\boldsymbol{\textit{E}}(G)$表示其邻接能量，$\boldsymbol{\textit{\u03b1}}(G)$表示其独立数。Kumar和Pragada新近的定理指出：$\boldsymbol{\textit{E}}(G)\u22652(n-\boldsymbol{\textit{\u03b1}}(G))$。本文确定了所有达到等号的图，更准确地说，等号成立当且仅当$G$的每个连通分支为孤立顶点、平衡完全多部图，或由$K_{a,\u2026,a}$与$K_{b,\u2026,b}$（两者均有$r\u22653$个相同数目的部分）的不交并经完全连接对应部分得到的图。
英文摘要
For a graph $G$ of order $n$, let $\mathcal E(G)$ denote its adjacency energy and let $α(G)$ denote its independence number. A recent theorem of Kumar and Pragada states that $$\mathcal E(G)\ge 2\bigl(n-α(G)\bigr).$$ 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.
