A New Method to Find the Wiener Index of Hypergraphs

Abstract

The Wiener index is defined as the summation of distances between all pairs of vertices in a graph or in a hypergraph. Both models—graph-theoretical and hypergraph-theoretical—are used in mathematical chemistry for quantitatively studying physical and chemical properties of classical and nonclassical organic compounds. In this paper, we consider relationships between hypertrees and trees and hypercycles and cycles with respect to their Wiener indices.

Graceful Labeling of Hypertrees

“…A graph G that admits a graceful labeling is called a graceful labeling. Definition 2.1 (Yalan, 2020): Consider a k-uniform hypertree with at most two vertices whose degrees are not less than 2 in each edge of . Any two edges with at most one common vertex is called a joint vertex, otherwise this vertex is called non-joint.…”

The cut method on hypergraphs for the Wiener index

“…In [30] the authors investigate, among others, 3uniform paths and lower bounds on the Wiener index of k-uniform hypergraphs. In [12,22] hypergraphs are constructed from trees and their Wiener index investigated. The effect of some transformations on the Wiener index of a hypergraph and extremal hypertrees with respect to the Wiener index is studied in [25].…”