Armenian Journal of Mathematics, 10(2)
ISSN 1829-1163
2022; 1–11
Shared with The Gufo

Perfect 3-colorings of Cubic Graphs of Order 8

Mehdi Alaeiyan*, Ayoob Mehrabani

Received: 2024-12-12 · Published: 2022-09-19

© 2022 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
Shared article.

Originally published in Armenian Journal of Mathematics, 10(2), 2022 — https://doi.org/10.52737/18291163-2018.10.2-1-11.

Original title
Perfect 3-colorings of Cubic Graphs of Order 8
Authors
Mehdi Alaeiyan, Ayoob Mehrabani
Source journal
Armenian Journal of Mathematics, 10(2)
Published
2022-09-19
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2018.10.2-1-11

Abstract

Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect mm-coloring of a graph GG with mm colors is a partition of the vertex set of GG into m parts A1A1, ……, AmAm such that, for all i,j∈{1,⋯,m}i,j∈{1,⋯,m}, every vertex of AiAi is adjacent to the same number of vertices, namely, aijaij vertices, of AjAj . The matrix A=(aij)i,j∈{1,⋯,m}A=(aij)i,j∈{1,⋯,m} 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 88. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 8.
1 / ? 100% Open in new tab Download Cite

Loading the full text…

Download Follow Updates