There are Finitely Many Triangle-Free Distance-Regular Graphs with Degree 8, 9 or 10
نویسنده
چکیده
In this paper we prove that there are finitely many triangle-free distance-regular graphs with degree 8, 9 or 10.
منابع مشابه
Two theorems concerning the Bannai-Ito conjecture
In 1984 Bannai and Ito conjectured that there are finitely many distance-regular graphs with fixed valencies greater than two. In a series of papers, they showed that this is the case for valency 3 and 4, and also for the class of bipartite distance-regular graphs. To prove their result, they used a theorem concerning the intersection array of a triangle-free distance-regular graph, a theorem t...
متن کاملSe p 20 09 There are only finitely many distance - regular graphs of fixed valency greater than two
There are only finitely many distance-regular graphs of fixed valency greater than two Abstract In this paper we prove the Bannai-Ito conjecture, namely that there are only finitely many distance-regular graphs of fixed valency greater than two.
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In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2 k ≤ C. This extends a conjecture of Bannai and Ito.
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Article history: Received 12 September 2007 Available online 9 August 2008
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