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Question What is the difference between generalized service area polygons and detailed service area polygons? Answer Generalized and detailed service area polygons are differentiated by the methods used to generate them, the amount of time it takes to generate them, as well as their relative overall accuracy of network coverage.
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Generalized Polygons - PDF Free Download
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We say a generalized polygon is thick if every point line is incident with at least three lines points. All thick generalized polygons have an order.
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It can easily be shown that this is again a generalized n -gon. Generalized "n"-gons for these values are referred to as generalized digons, triangles, quadrangles, hexagons and octagons. When Feit-Higman theorem is combined with the Haemers-Roos inequalities, we get the following restrictions,.
If s and t are both infinite then generalized polygons exist for each n greater or equal to 2. It is unknown whether or not there exist generalized polygons with one of the parameters finite and bigger than 1 while the other infinite these cases are called semi-finite.
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Peter Cameron proved the non-existence of semi-finite generalized quadrangles with three points on each line, while Andries Brouwer and Bill Kantor independently proved the case of four points on each line. The non-existence result for five points on each line was proved by G. Cherlin using Model Theory. As noted before the incidence graphs of generalized polygons have important properties.
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They are also related to expander graphs as they have nice expansion properties. Listen to this article Thanks for reporting this video! Volume 6 Issue 4 Oct , pp.
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Previous Article. Next Article. The Euclidean distortion of generalized polygons. Abstract We determine the Euclidean distortion of finite generalized polygons by means of semidefinite programing. About the article Received : Published Online : Published in Print : Related Content Loading General note: By using the comment function on degruyter. A respectful treatment of one another is important to us.