The design spectrum of the Shrikhande graph

Anthony D. Forbes; Carrie G. Rutherford

The design spectrum of the Shrikhande graph

Combinatorics 2025-08-05 v2

Authors: Anthony D. Forbes , Carrie G. Rutherford

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

Keywords

design spectrum Shrikhande graph edge decomposition complete graph line graph graph decomposition

Cite

@article{arxiv.2505.00859,
  title  = {The design spectrum of the Shrikhande graph},
  author = {Anthony D. Forbes and Carrie G. Rutherford},
  journal= {arXiv preprint arXiv:2505.00859},
  year   = {2025}
}

Comments

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

The design spectrum of the Shrikhande graph

Abstract

Keywords

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