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arXiv · 2012.00466

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

Deisiane Lopes Gonçalves·Bhalchandra D. Thatte
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Abstract

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

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Deisiane Lopes Gonçalves, Bhalchandra D. Thatte. 2020-12-01. A construction of the abstract induced subgraph poset of a graph from its abstract edge subgraph poset. https://arxiv.org/abs/2012.00466

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