Brouwer, Andries E. Classification of small \((0,2)\)-graphs. (English) Zbl 1105.05009 J. Comb. Theory, Ser. A 113, No. 8, 1636-1645 (2006). Summary: We find the graphs of valency at most 7 with the property that any two nonadjacent vertices have either 0 or 2 common neighbours. In particular, we find all semibiplanes of block size at most 7. Cited in 11 Documents MSC: 05B25 Combinatorial aspects of finite geometries 51E24 Buildings and the geometry of diagrams 05C62 Graph representations (geometric and intersection representations, etc.) 05B05 Combinatorial aspects of block designs 05C30 Enumeration in graph theory Keywords:semibiplanes; block PDFBibTeX XMLCite \textit{A. E. Brouwer}, J. Comb. Theory, Ser. A 113, No. 8, 1636--1645 (2006; Zbl 1105.05009) Full Text: DOI References: [1] Brouwer, A. E.; Cohen, A. M.; Neumaier, A., Distance-Regular Graphs (1989), Springer-Verlag: Springer-Verlag Berlin · Zbl 0747.05073 [2] Hughes, D. R., Biplanes and semi-biplanes, (Combinatorial Mathematics, Proc. Internat. Conf. Combinatorial Theory. Combinatorial Mathematics, Proc. Internat. Conf. Combinatorial Theory, Australian Nat. Univ., Canberra, 1977. Combinatorial Mathematics, Proc. Internat. Conf. Combinatorial Theory. Combinatorial Mathematics, Proc. Internat. Conf. Combinatorial Theory, Australian Nat. Univ., Canberra, 1977, Lecture Notes in Math., vol. 686 (1978), Springer-Verlag: Springer-Verlag Berlin), 55-58 · Zbl 0418.05010 [3] Janko, Zvonimir; Van Trung, Tran, Two new semibiplanes, J. Combin. Theory Ser. A, 33, 102-105 (1982) · Zbl 0485.05019 [4] Michel Mollard, Table of \((0, 2)\); Michel Mollard, Table of \((0, 2)\) [5] Moorhouse, G. Eric, Reconstructing projective planes from semibiplanes, (Coding Theory and Design Theory, Part II. Coding Theory and Design Theory, Part II, IMA Vol. Math. Appl., vol. 21 (1990), Springer-Verlag: Springer-Verlag New York), 280-285 · Zbl 0724.51012 [6] H.M. Mulder, The interval function of a graph, PhD thesis, Vrije Universiteit Amsterdam, 1980; H.M. Mulder, The interval function of a graph, PhD thesis, Vrije Universiteit Amsterdam, 1980 · Zbl 0446.05039 [7] Neumaier, A., Rectagraphs, diagrams, and Suzuki’s sporadic simple group, (Algebraic and Geometric Combinatorics. Algebraic and Geometric Combinatorics, North-Holland Math. Stud., vol. 65 (1982), North-Holland: North-Holland Amsterdam), 305-318 · Zbl 0491.05033 [8] P.R. Wild, On semibiplanes, PhD thesis, University of London, 1980; P.R. Wild, On semibiplanes, PhD thesis, University of London, 1980 [9] Wild, Peter, Generalized Hussain graphs and semibiplanes with \(k \leqslant 6\), Ars Combin., 14, 147-167 (1982) · Zbl 0504.05021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.