标题： 从图的抽象边子图序集构造图的抽象诱导子图序集 显示英文标题

标题： A construction of the abstract induced subgraph poset of a graph from its abstract edge subgraph poset

摘要： 一个图的抽象诱导子图偏序集是该图的诱导子图偏序集的同构类，适当通过子图计数数进行加权。 抽象键格和抽象边子图偏序集则通过考虑由连通划分诱导的子图格和边子图的偏序集分别定义。 继续我们在这些结构上的图重构理论的发展，我们证明如果一个图没有孤立顶点，那么它的抽象键格和抽象诱导子图偏序集可以从抽象边子图偏序集构造出来，除了我们所表征的图族。 从抽象边子图偏序集构造抽象诱导子图偏序集的方法推广了一个在重构理论中众所周知的结果，该结果指出，对于至少有4条边且没有孤立顶点的图，其顶点牌组可以从其边牌组构造出来。12 显示英文摘要

摘要： The abstract induced subgraph poset of a graph is the isomorphism class of the induced subgraph poset of the graph, suitably weighted by subgraph counting numbers. The abstract bond lattice and the abstract edge-subgraph poset are defined similarly by considering the lattice of subgraphs induced by connected partitions and the poset of edge-subgraphs, respectively. Continuing our development of graph reconstruction theory on these structures, we show that if a graph has no isolated vertices, then its abstract bond lattice and the abstract induced subgraph poset can be constructed from the abstract edge-subgraph poset except for the families of graphs that we characterise. The construction of the abstract induced subgraph poset from the abstract edge-subgraph poset generalises a well known result in reconstruction theory that states that the vertex deck of a graph with at least 4 edges and without isolated vertices can be constructed from its edge deck.12