چكيده به لاتين
In this thesis, we introduce perfect m-colorings. A perfect coloring is a generalization
of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a
graph G with m colors is a partition of the vertex set of G into m parts A1, . . . , Am
such that, for all i; j 2 f1; : : : ;mg, every vertex of Ai is adjacent to the same number
of vertices, namely, aij vertices, of Aj . The matrix A = (aij)i;j2f1;:::;mg, is called the
parameter matrix. This thesis contains two parts. In the first part we study the perfect
2-colorings (also known as the equitable partitions into two parts) of the cubic graph of
order less than 10 and Heawood, GraphPlatonic graphs. In the second part, we study the
perfect 2-colorings (also known as the equitable partitions into three parts) of the cubic
graph of order 8 and 10, the Platonic graphs and Heawood Graph. Also, some other results
are obtained for more graphs.
