This Msc. thesis is based on the following paper Devos, M., Goddyn, L., Mohar, B., Samal, R., Cayley sum graphs and eigenvalues of (3,6)- fullerenes, Journals of Combinatorial Theory, Series B 99 (2009) 358-369. Let G be a group and S be an arbitrary subset of G. The Cayley sum graph over with respect to is a graph with vertex set V=G and edge set . Let e a graph with vertices labeled as . The adjacency matrix of is an matrix with -entery equals to 1 if vertices and are adjacent and 0 otherwise. The spectrum of a graph is the set of numbers which are eigenvalues of , together with their multiplicities. We shall usually refer to the eigenvalues of as the eigenvalues of <v:imagedata src="file:///C:\\DOCUME~1\\M4F6A~1.HAJ\\LOCALS~1\emp\\msohtmlclip1\\01\\clip_image015.png" chromakey=