Total perfect codes in Cayley graphs
Abstract
A total perfect code in a graph is a subset of such that every vertex of is adjacent to exactly one vertex in . We give necessary and sufficient conditions for a conjugation-closed subset of a group to be a total perfect code in a Cayley graph of the group. As an application we show that a Cayley graph on an elementary abelian -group admits a total perfect code if and only if its degree is a power of . We also obtain necessary conditions for a Cayley graph of a group with connection set closed under conjugation to admit a total perfect code.
Cite
@article{arxiv.1601.03471,
title = {Total perfect codes in Cayley graphs},
author = {Sanming Zhou},
journal= {arXiv preprint arXiv:1601.03471},
year = {2018}
}
Comments
This is the final version published in: Designs, Codes and Cryptography 81 (2016) 489-504. The surname of the first author of [8] in the previous version (which is [7] in this version) was mistakenly spelt as Dejtera. The correct form should be Dejter, and in the present version this typo has been corrected