论文标题
迭代跳跃图
Iterated Jump Graphs
论文作者
论文摘要
简单图$ g $的跳跃图$ j（g）$具有$ g $中的边缘，其中$ j（g）$中的两个顶点在且仅当$ g $中的相应边缘不共享端点时，才相邻。在本文中，我们检查了通过迭代跳跃图操作而生成的图的序列，并表征所有初始图的该序列的行为。我们以Chartrand等人的工作为基础。他们表明少数跳图序列终止，两个序列会收敛。我们通过表明没有跳跃图的非平凡重复序列来扩展这些结果。所有不同的跳跃图序列在累积某些子图的同时就不会生长。
The jump graph $J(G)$ of a simple graph $G$ has vertices which represent edges in $G$ where two vertices in $J(G)$ are adjacent if and only if the corresponding edges in $G$ do not share an endpoint. In this paper, we examine sequences of graphs generated by iterating the jump graph operation and characterize the behavior of this sequence for all initial graphs. We build on work by Chartrand et al. who showed that a handful of jump graph sequences terminate and two sequences converge. We extend these results by showing that there are no non-trivial repeating sequences of jump graphs. All diverging jump graph sequences grow without bound while accumulating certain subgraphs.
