Abstract
A perfect coloring of a graph G with m color (a perfect mcoloring) is a surjective mapping P : V (G) → {1, 2, . . . , m} such that each vertex of color i has exactly mij neighbors of color j, for all i, j, where M = (mij )i,j=1,2,...,m is the corresponding matrix. In this paper, we classify perfect 2-colorings of the bicubic graphs with order up to 12.

Somayeh Shafiee Alamoti, Mehdi Alaeiyan, Alireza Gilani, Maryam Golriz. (2020) On Perfect 2-Coloring of the Bicubic Graphs with Order up to 12, Punjab University Journal of Mathematics, Volume 52 , Issue No 8.
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