Abstract

Due to Feit and Higman [12], the (thick) generalized $n$-gons exist only for $n \in \{ 2, 3, 4, 6, 8\}$ and are apparently quite rare for $n=6$ or $8$. By virtue of the above fact, in this article, we investigate the generalized polygons which are strongly regular graphs and pseudo geometric graphs. Also, we obtain the parameters of partial geometry and partially balanced incomplete block (PBIB) designs with association scheme arising from classical graph theoretic parameters (covering, independence, domination and neighborhood number) on generalized polygons.

Keywords and Phrases

Graph, partial geometry, generalized polygons, pseudogeometric graph, partially balanced incomplete block design.

A.M.S. subject classification

05E30, 51E12, 51E14.

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