Abstract: A set of vertices (or the code) in a graph is called strongly distance invariant if for any three non-negative integers the number of triangles in the set with one fixed point and with these three legs does not depends on the choice of the point. It is known that every fiber of an equitable partition (in particular, every completely regular code) in the Hamming graph is strongly distance invariant. But this property cannot be generalized to equitable partitions of an arbitrary distance-regular graph. A Steiner quadruple system (SQS(n)) is a set of 4-subsets of an n-set such that every 3-subset is contained in exactly one 4subset of the system; an SQS(n) is a completely regular code in the Johnson graph. We show that for infinitely many n there exists an SQS(n) that is not strongly distance invariant.

Cite: Krotov D.S. , Vasil'eva A.
On Strong Distance Invariance of Some Steiner Quadruple Systems
In compilation 2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY). 2023. – C.159 - 162. DOI: 10.1109/Redundancy59964.2023.10330167 Scopus OpenAlex

Dates:

Published print:	Dec 4, 2023
Published online:	Dec 4, 2023

Identifiers:

Scopus:	2-s2.0-85180157048
OpenAlex:	W4389297813

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