A perfect coloring of a graph G with m color (a perfect mcoloring) is a surjective mapping P : V (G) → {1, 2, . . . , m} such thateach 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.

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.