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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 A_1, A_2, ..., A_m such that, for all i,jβ{1,...,m}, every vertex of A_i is adjacent to the same number of vertices, namely, a_{ij} vertices, of A_j. The matrix A=(aijβ)i,jβ{1,...,m}β, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the cubic graphs of order 10. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 10
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