Projects per year
Abstract
In this paper, we consider the question of when a strongly regular graph with parameters ((s+1)(st+1),s(t+1),s−1,t+1) can exist. A strongly regular graph with such parameters is called a pseudo-generalized quadrangle. A pseudo-generalized quadrangle can be derived from a generalized quadrangle, but there are other examples which do not arise in this manner. If the graph is derived from a generalized quadrangle then t≤s2 and s≤t2, while for pseudo-generalized quadrangles we still have the former bound but not the latter. Previously, Neumaier has proved a bound for s which is cubic in t, but we improve this to one which is quadratic. The proof involves a careful analysis of cliques and cocliques in the graph. This improved bound eliminates many potential parameter sets which were otherwise feasible.
Original language | English |
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Article number | 103128 |
Number of pages | 9 |
Journal | European Journal of Combinatorics |
Volume | 89 |
DOIs | |
Publication status | Published - Oct 2020 |
Projects
- 3 Finished
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The role of liquidity in financial markets
Zhu, S.-P. (Primary Chief Investigator (PCI)), Elliott, R. J. (Chief Investigator (CI)) & Guo, I. (Chief Investigator (CI))
15/06/17 → 31/12/20
Project: Research
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Planar Brownian motion and complex analysis
Markowsky, G. (Primary Chief Investigator (PCI))
Australian Research Council (ARC)
2/01/14 → 11/01/17
Project: Research
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New Stochastic Processes with Applications in Finance
Klebaner, F. (Primary Chief Investigator (PCI)), Buchmann, B. (Chief Investigator (CI)) & Hamza, K. (Chief Investigator (CI))
Australian Research Council (ARC), Monash University
31/07/09 → 31/12/13
Project: Research