A non-existence theorem for (v, k,λ)-graphs
1970 ◽
Vol 11
(3)
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pp. 381-383
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A (ν, κ, λ)-graph is defined in [3] as a graph on ν points, each of valency κ, and such that for any two points P and Q there are exactly λ points which are joined to both. In other words, if Si is the set of points joined to Pi, thenSi has k elements for any iSiSj has λ elements if i≠jThe sets Si are the blocks of a (v, k, λ)-configuration, so a necessary condition on v, k, and λ that a graph should exist is that a (v, k, λ)- configuration should exist. Another necessary condition, reported by Bose (see [1]) and others, is that there should be an integer m satisfying have equal parity. We shall prove that these conditions are not sufficient.
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1935 ◽
Vol 4
(3)
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pp. 112-117
1933 ◽
Vol 29
(2)
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pp. 207-211
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1989 ◽
Vol 32
(3)
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pp. 483-494
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1987 ◽
Vol 28
(3)
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pp. 376-392
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1970 ◽
Vol 22
(1)
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pp. 61-65
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Keyword(s):
1935 ◽
Vol 4
(2)
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pp. 80-84
1988 ◽
Vol 40
(3)
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pp. 589-609
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