Wiener index of uniform hypergraphs induced by trees
ODAM-Vol. 2 (2019), Issue 3, pp. 19 – 22 Open Access Full-Text PDF
Andrey Alekseevich Dobrynin
Abstract: The Wiener index \(W(G)\) of a graph \(G\) is defined as the sum of distances between its vertices. A tree \(T\) generates \(r\)-uniform hypergraph \(H_{r,k}(T)\) by the following way: hyperedges of cardinality \(r\) correspond to edges of the tree and adjacent hyperedges have \(k\) vertices in common. A relation between quantities \(W(T)\) and \(W(H_{r,k}(T))\) is established.