Edge reconstruction and the swapping number of a graph
Dalibor Fronček, Amy Lee Hlavacek, Steven Rosenberg · 2014
We define the swapping number of an arbitrary simple graph, which is related to edge reconstruction, and involves a weakening of the concept of a graph automorphism. We classify all 1-swappable trees and unicyclic graphs and prove that the expected value of the swapping number grows linearly with the order of the graph.