Šoltés' hypergraphs
arXiv:2406.01504
Abstract
More than years ago, Šoltés observed that the total distance of the graph does not change by deleting a vertex, and wondered about the existence of other such graphs, called Šoltés graphs. We extend the definition of Šoltés' graphs to Šoltés' hypergraphs, determine all orders for which a Šoltés' hypergraph exists, observe infinitely many uniform Šoltés' hypergraphs, and find the Šoltés' hypergraph with minimum size (spoiler: it is not ).
11 pages, 6 figures