New Polynomial-Based Molecular Descriptors with Low Degeneracy

Matthias Dehmer,Laurin A J Mueller,Armin Graber,Fabio Rapallo

doi:10.1371/journal.pone.0011393

Abstract

In this paper, we introduce a novel graph polynomial called the ‘information polynomial’ of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power.

Highlights

The study of specific structural properties of graphs by using algebraic polynomial representations has been a well-known and fruitful concept for several decades [1,2,3,4,5,6]
The aim of this section is to evaluate the just defined descriptors in terms of their uniqueness [31,32]. This property of a molecular descriptor relates to the ability to distinguish graphs as uniquely as possible by calculating the underlying graph measure
We summarize the main findings of our paper and some future ideas as follows: N We started from the idea to use the probability distribution

Summary

Introduction

The study of specific structural properties of graphs by using algebraic polynomial representations has been a well-known and fruitful concept for several decades [1,2,3,4,5,6]. Graph polynomials have been either used for describing combinatorial graph invariants or to characterize chemical structures by using the coefficients or the zeros of a graph polynomial [4,7,8]. A very important graph polynomial is the characteristic polynomial of a graph which has been intensely studied by Cvetkovic [10] when exploring structural properties of a graph related to its eigenvalues. Have been developed for investigating multifaceted aspects of chemical structures Afterwards, various other graph polynomials [8,9,11] such as the Laplacian polynomial, Matching polynomial, Muhlheim polynomial, Distance polynomial and the Wiener Polynomial etc. have been developed for investigating multifaceted aspects of chemical structures

Methods

Results

Conclusion