The Distance-Regular Graphs of Valency Four
A.E. Brouwer
and J.H. Koolen
DOI: 10.1023/A:1018693118268
Abstract
Pages: 5–24
Keywords: distance-regular graph in this note we report on a computer search that proves that each distance-regular graph of valency four has known parameters
Full Text: PDF
References
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1989. A.M. Cohen and J. Tits, On generalized hexagons and a near octagon whose lines have three points, Eur. J. Combin. 6 (1985), 13-27. A. Hiraki, An improvement of the Boshier-Nomura bound, J. Combin. Th. (B) 61 (1994), 1-4. A. Hiraki, A Constant Bound for the Number of Columns (1, k - 2, 1) in the Intersection Array of Distance-Regular Graph, Graphs and Combinatorics 12 (1996), 23-37. L. Kronecker, Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten, Crelle, Journal f. d. reine u. angew. Math. 53 (1857), 173-175. Also found in Leopold Kronecker”s Werke, K. Hensel (Ed.), Chelsea reprint, 1968, pp. 105-108. B. Mohar and J. Shawe-Taylor, Distance-biregular graphs with 2-valent vertices and distance-regular line graphs, J. Combin. Th. (B) 38 (1985), 193-203. K. Nomura, Distance-regular graphs with valency four and girth three, preprint. K. Nomura, email communication, 16 May
1992. K. Nomura, A remark on bipartite distance-regular graphs of even valency, Graphs and Combinatorics 11 (1995), 139-140. I. Schur, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahlichen Koef-fizienten, Math. Zeitschrift 1 (1918), 377-402. Also found in Issai Schur, Gesammelte Abhandlungen, Alfred Brauer and Hans Rohrbach (Eds.), Springer, Berlin, 1973, Band 2, pp. 213-238. H. Suzuki, On Distance-Biregular Graphs of Girth Divisible by Four, preprint. P. Terwilliger, Eigenvalue multiplicities of highly symmetric graphs, Discrete Math. 41 (1982), 295-302.