Perfect 3-Colorings on 4-Regular Graph of Order 8

S. Maity¹ , Sk. R. Islam²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.137-142, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.137142

Online published on Dec 31, 2018

Copyright © S. Maity, Sk. R. Islam . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
We study the perfect 3-colorings (also known as the equitable partitions into three parts) on 4-regular graphs of order 8. A perfect n-coloring of a graph is a partition of its vertex set into n parts A1, A2, ..., An such that for all p, q ϵ {1, 2,..., n}, each vertex of Ap is adjacent to apq number of vertices of Aq. The matrix A = (apq) n×n is called quotient matrix or parameter matrix. The concept of a perfect coloring generalizes the concept of completely regular code introduced by P. Delsarte. In particular, we classify all the realizable parameter matrices of perfect 3-colorings on 4-regular graphs of order 8.

Key-Words / Index Term :
Perfect colorings; equitable partition; regular graph

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