Shahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231441-220140601On the spectrum of Cayley graphs via character table11147710.22061/jmns.2014.477ENFarzanehNowrooziDepartment of Mathematics, Faculty of Science, Shahid RajaeeTeacher Training University, Tehran, 16785 – 136, I R. IranModjtabaGhorbaniDepartment of Mathematics, Faculty of Science, Shahid RajaeeTeacher Training University, Tehran, 16785 – 136, I R. IranJournal Article20130706A Cayley graph can be consider as an interpretation of group representation. This means that one can construct the Cayley graph Г = Cay(G, S) by having the vertex set to be the elements of G with g~h if and only if hg<sup>-1</sup> ε S. In this paper, we focus our attention on Cayley graphs with a normal symmetric subset. We also determine all eigenvalues of Buckminster fullerene by constructing Cay(G,S) where G is the alternating group A<sub>5</sub>.http://jmathnano.sru.ac.ir/article_477_166922038b274bc7128566c1e2ce4b98.pdf