The packing number of the double vertex graph of the path graph
Combinatorics
2023-07-14 v3
Abstract
Neil Sloane showed that the problem of determine the maximum size of a binary code of constant weight 2 that can correct a single adjacent transposition is equivalent to finding the packing number of a certain graph. In this paper we solve this open problem by finding the packing number of the double vertex graph (2-token graph) of a path graph. This double vertex graph is isomorphic to the Sloane's graph. Our solution implies a conjecture of Rob Pratt about the ordinary generating function of sequence A085680.
Cite
@article{arxiv.1711.03682,
title = {The packing number of the double vertex graph of the path graph},
author = {José Manuel Gómez Soto and Jesús Leaños and Luis Manuel Ríos-Castro and Luis Manuel Rivera},
journal= {arXiv preprint arXiv:1711.03682},
year = {2023}
}
Comments
21 pages, 7 figures. V2: 22 pages, more figures added. V3. minor corrections based on referee's comments. One figure corrected. The title "On an error correcting code problem" has been changed