A Higman inequality for regular near polygons

Autor: Frédéric Vanhove
Rok vydání: 2011
Předmět:
Zdroj: Journal of Algebraic Combinatorics. 34:357-373
ISSN: 1572-9192
0925-9899
DOI: 10.1007/s10801-011-0275-7
Popis: The inequality of Higman for generalized quadrangles of order (s,t) with s>1 states that t?s 2. We generalize this by proving that the intersection number c i of a regular near 2d-gon of order (s,t) with s>1 satisfies the tight bound c i ?(s 2i ?1)/(s 2?1), and we give properties in case of equality. It is known that hemisystems in generalized quadrangles meeting the Higman bound induce strongly regular subgraphs. We also generalize this by proving that a similar subset in regular near 2d-gons meeting the bounds would induce a distance-regular graph with classical parameters (d,b,?,β)=(d,?q,?(q+1)/2,?((?q) d +1)/2) with q an odd prime power.
Databáze: OpenAIRE
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