International Journal of Nonlinear Analysis and Applications

Perfect 3-colorings of Heawood graph

Document Type : Research Paper

Author

School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran

Abstract

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 $A_1, . . . , A_m$ such that, for all $i, j \in \{1, . . . , m\}$, every vertex of $A_i$ is adjacent to the same number of vertices, namely, $a_{ij}$ vertices, of $A_j$. The matrix $A = (a_{ij} )$, $i, j \in \{1, 2,... , m\}$, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the Heawood graph. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the Haywood graphs.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 713-717
  • Receive Date: 08 October 2018
  • Revise Date: 02 June 2019
  • Accept Date: 07 June 2019