某些标准图的迂回单色顶点覆盖数（DMVCPN）
Detour Monophonic Vertex Cover Pebbling Number (DMVCPN) of Some Standard Graphs
AI总结：
本文定义了通过迂回单色路径进行 pebble 转换以覆盖顶点覆盖集的 detour monophonic vertex cover pebbling number，并确定了圈图、路径图、扇图和轮图的该数值。
摘要：
设 $G$ 为连通图，顶点集为 $V(G)$，边集为 $E(G)$。Pebbling shift 是指从一个顶点删除两个 pebble 并在相邻顶点放置一个 pebble。图 $G$ 的顶点覆盖集 $D_{vc}$ 是 $V(G)$ 的子集，使得 $G$ 中每条边至少有一个端点在 $D_{vc}$ 中。Detour monophonic path 是指两个不相邻顶点 $x$ 和 $y$ 之间的最长无弦路径。Detour monophonic vertex cover pebbling number $μ_{vc}(G)$ 是指通过使用 detour monophonic paths 进行 pebble 转换后，使 $G$ 的顶点覆盖集所有顶点各至少有一个 pebble 所需的最小 pebble 数。我们确定了圈图、路径图、扇图和轮图的 detour monophonic vertex cover pebbling number (DMVCPN)。
英文摘要：
Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Pebbling shift is a deletion of two pebbles from a vertex and a placement of one pebble at a neighbouring vertex. The vertex cover set, $D_{vc}$ for graph $G$ is the subset of $V(G)$ such that every edge in $G$ has at least one end in $D_{vc}$. A detour monophonic path is considered to be a longest chordless path between two non adjacent vertices $x$ and $y$. A detour monophonic vertex cover pebbling number, $μ_{vc}(G),$ is a minimum number of pebbles required to cover all the vertices of the vertex cover set of $G$ with at least one pebble each on them after the transformation of pebbles by using detour monophonic paths. We determine the detour monophonic vertex cover pebbling number (DMVCPN) of the cycle, path, fan, and wheel graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
