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The Simultaneous Metamorphosis of Small-Wheel Systems

Peter Adams1, Elizabeth J. Billington 1, E.S. Mahmoodian 2
1Centre for Discrete Mathematics and Computing, Department of Mathematics, The University of Queensland, Queensland 4072 AUSTRALIA
2 Department of Mathematical Sciences Sharif University of Technology P.O. Box 11365-9415 Tehran, LR. IRAN

Abstract

Metamorphoses of small k-wheel systems for k=3,4, and 6 are obtained. In particular, we obtain simultaneous metamorphoses of: 3-wheel systems into Steiner triple systems and into K1,3-designs; 4-wheel systems into 4-cycle systems, K1,4-designs, and bowtie systems; 6-wheel systems into 6-cycle systems, K1,6-designs, and 3-windmill designs or near-3-windmill designs.