The inverse problem for the Steiner--Wiener index via additive number theory

TL;DR

This paper proves that for any fixed k ≥ 2, all sufficiently large numbers can be realized as the Steiner--Wiener k index of some graph, connecting graph invariants with additive number theory.

Contribution

It establishes the inverse problem for the Steiner--Wiener index, demonstrating the universality of large numbers as index values through additive number theory techniques.

Findings

Every sufficiently large number is the Steiner--Wiener k index of some graph for fixed k ≥ 2.

The result links graph invariants with additive number theory.

Provides a method to construct graphs with prescribed Steiner--Wiener indices.

Abstract

We show that, for any given $k \ge 2$, every sufficiently large number appears as the Steiner--Wiener $k$ index of a graph.