The design spectrum of the Shrikhande graph

2025/05/01 by Anthony D. Forbes, Forbes, Anthony D., Carrie Rutherford +1
Computer Science · Engineering · Mathematics · #05B25 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2505.00859

openalex publication_date 2025/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The design spectrum of a simple graph G is the set of positive integers n such that there exists an edgewise decomposition of the complete graph K_n into n(n - 1)/(2 |E(G)|) copies of G. The purpose of this short paper is to prove that the Shrikhande graph and the line graph of K_4,4 have the design spectrum \96t + 1: t = 1, 2, …\.

Citations

• Design spectra for 6-regular graphs with 12 vertices

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