Perfect 3-colorings of the cubic graphs of order 10
| Main Authors: | Alaeiyan, Mehdi; School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran, Mehrabani, Ayoob; School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2017
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/316 http://www.ejgta.org/index.php/ejgta/article/view/316/pdf_48 http://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/316/46 |
Daftar Isi:
- 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.