Zeinab Vahedi - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Mohammad Maghasedi - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Mehdi Alaeiyan - Iran University of Science and Technology

The perfect m-coloring with matrix A = [aij ]i,j∈{۱,...,m} of a graph G = (V, E) with {۱, . . . , m} color is a vertices coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is aij , independent of the choice of vertex in color i. The matrix A = [aij ]i,j∈{۱,...,m} is called the parameter matrix.We study the perfect ۴-colorings of the ۳-regular graphs of order ۱۰, that is, we determine a list of all color parameter matrices corresponding to perfect colorings of ۳-regular graphs of order ۱۰. 

Perfect coloring, Parameter matrices, Cubic graph, Equitable partition