达到混合度量维数上界的图
Graphs attaining an upper bound on the mixed metric dimension
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中文总结 AI 辅助
该研究证明了混合度量维数达到上界的图的结构特征，对Sedlar等人2021年提出的猜想给出了肯定解答。
中文摘要 AI 辅助
给定图G，我们证明G的混合度量维数恰好为ℓ(G)+2c(G)当且仅当G是两类图之一：一是每个环恰有一个度数至少为3的顶点的仙人掌图，二是平衡Θ-图，其中ℓ(G)为G的叶子数，c(G)为G的环秩。这对Sedlar与Škrekovski（2021）提出的猜想给出了肯定解答。
英文摘要
Given a graph $G$, we show that the mixed metric dimension of $G$ is exactly $\ell(G)+2c(G)$ if and only if $G$ is either a cactus graph in which every cycle has precisely one vertex of degree at least $3$, or a balanced $Θ$-graph, where $\ell(G)$ and $c(G)$ denote the number of leaves and the cyclomatic number of $G$, respectively. This provides an affirmative answer to a conjecture proposed by Sedlar and Škrekovski (2021).
