A spectral proof of the uniqueness of a strongly regular graph with parameters (81, 20, 1, 6)
نویسندگان
چکیده
We give a new proof that there exists a unique strongly regular graph with parameters (81, 20, 1, 6). Unlike the finite geometry approach used by Brouwer and Haemers, we use linear algebra and spectral graph theory concepts, namely the technique of star complements, in our proof. AMS Classification: 05E30, 05C50
منابع مشابه
Structure and uniqueness of the (81, 20, 1, 6) strongly regular graph
Brouwer, A.E, W.H. Haemers, Structure and uniqueness of the (81,20, 1.6) strongly regular graph, Discrete Mathematics 106/107 (1992) 77-82. We prove that there is a unique graph (on 81 vertices) with spectrum 20’2”‘(-7)*“. We give several descriptions of this graph, and study its structure. Let r = (X, E) be a strongly regular graph with parameters (v, k, ;1, p) = (81, 20, 1, 6). Then r (that i...
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 30 شماره
صفحات -
تاریخ انتشار 2009