Enumerations of (K_4-e)-designs with small orders
Yanxun Chang, Tao Feng, Giovanni Lo Faro, and Antoinette Tripodi
TL;DR
This paper enumerates all non-isomorphic (K_4-e)-designs for small orders 6, 10, and 11, and explores their intersection properties, contributing to combinatorial design theory.
Contribution
It provides the first complete enumeration of (K_4-e)-designs for these small orders and applies these results to the fine triangle intersection problem.
Findings
Exactly one (K_4-e)-design of order 6
Three (K_4-e)-designs of order 10
Two (K_4-e)-designs of order 11
Abstract
It is established that up to isomorphism,there are only one (K_4-e)-design of order 6, three (K_4-e)-designs of order 10 and two (K_4-e)-designs of order 11. As an application of our enumerative results, we discuss the fine triangle intersection problem for (K_4-e)-designs of orders v=6,10,11.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Finite Group Theory Research