Searching Equienergetic Chemical Trees

This research aims to develop insight and algorithms to join the search for graphs with equal energy, regarding some possible definitions on what graph energy is. This research is made on a class of graphs called Chemical Trees, defined to be those which are acyclic and which each vertex has degree at most 4. High-performance code is to be developed, as this research, which is at initial stage (started Feb 2009), goes further.

The first interactive program can be found here. The corresponding C-code (called through a PHP interface) implements a call to CLapack routine dspev_ (computation of eigenvalues of symmetric matrix with packed storage).

The second interactive program can be found here. This script implements a search and classify procedure in a data set that we already have stored in a MySQL database.

Definitions of energy being used:

given a graph $G$ let $A$ be its adjacency matrix, let eig be the vector of eigenvalues of a given matrix, and $\vert\cdot\vert _1$ the 1-norm of a vector (sum of absolute values of its components).


$\displaystyle E (G) = \vert \mbox{eig}(A)\vert _1$
to be called just energy of graph $G$.

JBC 19/2/2009,13/5/2010