2015/12/18 by Leonard H. Soicher, Soicher, Leonard H. · 1 citation
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.1512.05976
It is known that, up to isomorphism, there is a unique distance-regular graph\n\Δ with intersection array 32,27;1,12 (equivalently, \Δ is the\nunique strongly regular graph with parameters (105,32,4,12)). Here we\ninvestigate the distance-regular antipodal covers of \Δ. We show that, up\nto isomorphism, there is just one distance-regular antipodal triple cover of\n\Δ (a graph Δ discovered by the author over twenty years ago),\nproving that there is a unique distance-regular graph with intersection array\n32,27,8,1;1,4,27,32. In the process, we confirm an unpublished result of\nSteve Linton that there is no distance-regular antipodal double cover of\n\Δ, and so no distance-regular graph with intersection array\n32,27,6,1;1,6,27,32. We also show there is no distance-regular antipodal\n4-cover of \Δ, and so no distance-regular graph with intersection array\n32,27,9,1;1,3,27,32, and that there is no distance-regular antipodal 6-cover\nof \Δ that is a double cover of Δ.\n