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

DOI10.1016/J.DISC.2021.112787zbMath1484.05207arXiv2301.06593MaRDI QIDQ6423543

Mojtaba Jazaeri

Publication date: 16 January 2023

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.

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Distance in graphs (05C12) Combinatorial codes (94B25)

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