2024/09/16 by Anthony D. Forbes, Forbes, Anthony, Carrie Rutherford +1
Decision Sciences · Engineering · #05B25 #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2409.10159
openalex publication_date 2024/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A regular-graph design is a block design for which a pair \a,b\ of distinct points occurs in λ+1 or λ blocks depending on whether \a,b\ is or is not an edge of a given δ-regular graph. Our paper describes a specific construction for regular-graph designs with λ= 1 and block size δ+ 1. We show that for δ∈ \2,3\, certain necessary conditions for the existence of such a design with n points are sufficient, with two exceptions in each case and two possible exceptions when δ= 3. We also construct designs of orders 105 and 117 for connected 4-regular graphs.