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.

Authors

  • S. S. Alamoti, M. Alaeiyan, A. Gilani , M. Golriz

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.

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Published

2025-05-15

Issue

Vol. 52 No. 8 (2020)

Section

Articles

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Copyright (c) 2020 S. S. Alamoti, M. Alaeiyan, A. Gilani , M. Golriz

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

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. (2025). Punjab University Journal of Mathematics, 52(8), 17-25. https://pujm.pu.edu.pk/index.php/pujm/article/view/364