A vertex distinguishes (or resolves) two elements (edges or vertices) if . A set of vertices in a nontrivial connected graph is said to be a mixed resolving set for if every two different elements (edges and vertices) of are distinguished by at least one vertex of . The mixed resolving set with minimum cardinality in is called the mixed metric dimension (vertex-edge resolvability) of and denoted by . The aim of this research is to determine the mixed metric dimension of some wheel graph subdivisions. We specifically analyze and compare the mixed metric, edge metric, and metric dimensions of the graphs obtained after the wheel graphs’ spoke, cycle, and barycentric subdivisions. We also prove that the mixed resolving sets for some of these graphs are independent.

中文翻译：

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一些轮相关图的顶点-边可解性

一个顶点 区分（或解析）两个元素（边或顶点） 如果 . 如果 的每两个不同元素（边和顶点）由 的至少一个顶点区分，则称非平凡连通图中的一组顶点是混合解析集。具有最小基数的混合解析集称为 的混合度量维度（顶点-边可解析性），用 表示。本研究的目的是确定一些轮图细分的混合度量维度。我们具体分析比较了轮图的辐条、周期和重心细分后得到的图的混合度量、边度量和度量维度。我们还证明了其中一些图的混合解析集是独立的。