perfect 3-colorings of the line graphs of the connected bicubic graphs of order at most 12

Let g = (vg, eg) be a graph and let i be a finite set of size m ≥ 1. a mapping t : vg → i is called a perfect m-coloring with a parameter matrix a = (aij)i,j∈i of g if it is surjective and for all i, j, every vertex of color i has aij neighbors of color j. in this paper, we classify all the realizable parameter matrices of perfect 3-colorings of the line graphs of the connected bicubic graphs of order at most 12.