Abstract
In this article the concept of graph coloration for factorization of the characteristic polynomial of a weighted directed graph is introduced and using the fundamental lemma of Petersdorf and Sachs, it is shown that this concept can be extended to other spectra of graph among which is the spectrum of the Laplacian matrix of graphs. The goal is to use this concept for factorizing the graphs having different types of symmetry properties. In order to present an efficient algorithm, some concepts from group theory are needed. The combination of group theory and graph coloration provides a powerful method for factorizing various structural matrices, an example of which is the stiffness matrices of mass-spring dynamic systems.
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