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J. J. Sylvester and F. Franklin, “A Constructive Theory of Partitions, Arranged in Three Acts, an Interact and an Exodion,” American Journal of Mathematics, Vol. 5, No. 1, 1882, pp. 251-330. doi:10.2307/2369545

has been cited by the following article:

• TITLE: A Graph-Theoretical Approach to Calculate Vibrational Energies of Atomic and Subatomic Systems

  AUTHORS: Jorge Galvez

  KEYWORDS: Graph Theory; Physical Systems; Vibrational Energy

  JOURNAL NAME: Open Journal of Physical Chemistry, Vol.2 No.4, November 26, 2012

  ABSTRACT: One of the challenges still pending in string theory and other particle physics related fields is the accurate prediction of the masses of the elementary particles defined in the standard model. In this paper an original algorithm to assign graphs to each of these particles is proposed. Based on this mapping, we demonstrate that certain indices associated with the topology of the graph (graph theoretical indices) are very effective in predicting the masses of the particles. Specifically, the spectral moments of the graph adjacency matrix weighted by edge degrees play a key role in the excellent correlations found. Moreover, the same topological pattern is found in other well known quantum systems such as the particle in a box and the vibrational frequencies of diatomic molecules, such as hydrogen. The results shown here open a suggestive pathway for the use of graph-theoretical approaches in predicting properties of elementary particles and other physical systems, which seem to match similar topological patterns.