Geodesic
Non-Existence Criteria for Small Configurations
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 213-215

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For graph theoretic terms, see Tutte [1], A rank 2 tactical configuration of girth 2g and order (s, t) may be regarded as a (1 + s, 1 + t)-regular bipartite graph of girth 2g. We assume s ≦ t. Using a technique of Friedman [2] we show (i) and (ii). 
Longyear, Judith Q. Non-Existence Criteria for Small Configurations. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 213-215. doi: 10.4153/CJM-1973-019-8
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[1] 1. Tutte, W., Connectivity in graphs (University of Toronto Press, Toronto, 1966). Google Scholar

[2] 2. Friedman, H., On the impossibility of certain Moore graphs, J. Combinatorial Theory 10B (1971), 245-253. Google Scholar

[3] 3. Feit, W. and Higman, G., The non-existence of certain generalized polygons, J. Algebra 1 (1964), 114–131. Google Scholar

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