Perfect 3-colorings of the Cubic Graphs of Order 10
2017  //  DOI: 10.5614/ejgta.2017.5.2.3
Mehdi Alaeiyan, Ayoob Mehrabani

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Perfect 3\u002Dcolorings of the Cubic Graphs of Order 10 Image
Abstrak

Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a graph G with m colors is a partition of the vertex set of G into m parts A_1, A_2, ..., A_m such that, for all $ i,j \in \lbrace 1, ... , m \rbrace $, every vertex of A_i is adjacent to the same number of vertices, namely, a_{ij} vertices, of A_j. The matrix $A=(a_{ij})_{i,j\in \lbrace 1,... ,m\rbrace }$, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the cubic graphs of order 10. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 10.

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  • Eye Icon 171 views
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Metrics Icon 171 views  //  116 downloads