Mathematical results on harmonic polynomials

TL;DR

This paper explores properties of harmonic polynomials associated with graphs, demonstrating how they can reveal graph similarities and aid in understanding the harmonic topological index.

Contribution

It introduces new properties of harmonic polynomials and establishes their ability to determine graph similarities and infer graph properties.

Findings

Harmonic polynomials can be used to deduce properties of graphs.

Graphs with identical harmonic polynomials are similar.

The paper provides bounds for the harmonic topological index.

Abstract

Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several properties of this polynomial, and we prove that several properties of graphs can be deduced from their harmonic polynomials. Also, we show that two graphs with the same harmonic polynomial have to be similar.