University of Technology-IraqEngineering and Technology Journal1681-690034520160528A General Formula for Characteristic Polynomials of Some Special Graphs638650124001ENNawras A. AlwanNadia M. G. Al-SaidiJournal Article20160501The calculation of characteristic polynomials (Ch. Poly.) of graphs of any size, especially for the large number of vertices n is an extremely tedious problem if used the traditional methods, so in this paper, the general formulas of the characteristic polynomial of some graphs, such as, path, complete, circle and star graphs are introduced. It is constructed based on adjacency and Laplacian matrices. The efficiency of the proposed method is demonstrated in terms of complexity to show an improvement over traditional methods.https://etj.uotechnology.edu.iq/article_124001_b8fcb207875c932bf0bb48f78e1100e6.pdf