Distance-regular graphs admitting a perfect $1$-code

Mojtaba Jazaeri

Distance-regular graphs admitting a perfect $1$-code

Combinatorics 2023-01-18 v1

Authors: Mojtaba Jazaeri

Abstract

In this paper, we study the problem that which of distance-regular graphs admit a perfect $1$ -code. Among other results, we characterize distance-regular line graphs which admit a perfect $1$ -code. Moreover, we characterize all known distance-regular graphs with small valency at most $4$ , the distance-regular graphs with known putative intersection arrays for valency $5$ , and all distance-regular graphs with girth $3$ and valency $6$ or $7$ which admit a perfect $1$ -code.

Keywords

graph theory graph pebbling random graphs

Cite

@article{arxiv.2301.06593,
  title  = {Distance-regular graphs admitting a perfect $1$-code},
  author = {Mojtaba Jazaeri},
  journal= {arXiv preprint arXiv:2301.06593},
  year   = {2023}
}

Comments

It has been published in the Discrete Mathematics journal

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