The design spectrum of the Shrikhande graph

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 $\{96t+1:t=1,2,\dots \}$.

5 pages. Section 3 updated; Theorem 3.2 added. The paper is under review. arXiv admin note: text overlap with arXiv:2401.02846