There does not exist a distance-regular graph with intersection array\n 80, 54,12; 1, 6, 60

2018/09/26 by Jack H. Koolen, Quaid Iqbal, Koolen, Jack H. +5
Biochemistry, Genetics and Molecular Biology · Engineering · #05C50 #05E30 #Combinatorics (math.CO) #FOS: Mathematics #NF-κB Signaling Pathways #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1809.10029

openalex publication_date 2018/09/26 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

In this paper we will show that there does not exist a distance-regular graph\n\Γ with intersection array 80, 54,12; 1, 6, 60 . We first show that\na local graph \Δ of \Γ does not contain a coclique with 5 vertices,\nand then we prove that the graph \Γ is geometric by showing that \Δ\nconsists of 4 disjoint cliques with 20 vertices. Then we apply a result of\nKoolen and Bang to the graph \Γ, and we could obtain that there is no\nsuch a distance-regular graph.\n

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