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arXiv · 2210.11184

On completely regular codes with minimum eigenvalue in geometric graphs

I. Yu. Mogilnykh·K. V. Vorob'ev
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Abstract

We prove that any completely regular code with minimum eigenvalue in any geometric graph G corresponds to a completely regular code in the clique graph of G. Studying the interrelation of these codes, a complete characterization of the completely regular codes in the Johnson graphs J(n,w) with covering radius w-1 and strength 1 is obtained. In particular this result finishes a characterization of the completely regular codes in the Johnson graphs J(n,3). We also classify the completely regular codes of strength 1 in the Johnson graphs J(n,4) with only one case for the eigenvalues left open.

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I. Yu. Mogilnykh, K. V. Vorob'ev. 2022-10-20. On completely regular codes with minimum eigenvalue in geometric graphs. https://arxiv.org/abs/2210.11184

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