Perfect 2-colorings of the cubic graphs of order less than or equal to 10

• Main Authors: Mehdi Alaeiyan, Ayoob Mehrabani
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2020-01-01
• Series: AKCE International Journal of Graphs and Combinatorics
• Subjects: perfect coloring; equitable partition; cubic graph; parameter matrix
• Online Access: http://dx.doi.org/10.1016/j.akcej.2018.11.004

Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect -coloring of a graph with colors is a partition of the vertex set of into m parts , . . . , such that, for all , every vertex of is adjacent to the same number of vertices, namely, vertices, of . The matrix , is called the parameter matrix. We study the perfect 2-colorings (also known as the equitable partitions into two parts) of the cubic graphs of order less than or equal to 10. In particular, we classify all the realizable parameter matrices of perfect 2-colorings for the cubic graphs of order less than or equal to 10.