Triangle-free distance-regular graphs with an eigenvalue multiplicity equal to their valency and diameter 3
نویسندگان
چکیده
منابع مشابه
Triangle-free distance-regular graphs with an eigenvalue multiplicity equal to their valency and diameter 3
In this paper, triangle-free distance-regular graphs with diameter 3 and an eigenvalue θ with multiplicity equal to their valency are studied. Let Γ be such a graph. We first show that θ = −1 if and only if Γ is antipodal. Then we assume that the graph Γ is primitive. We show that it is formally self-dual (and hence Q-polynomial and 1-homogeneous), all its eigenvalues are integral, and the eige...
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Let Γ be a triangle-free distance-regular graph with diameter d ≥ 3, valency k ≥ 3 and intersection number a2 6= 0. Assume Γ has an eigenvalue with multiplicity k. We show that Γ is 1-homogeneous in the sense of Nomura when d = 3 or when d ≥ 4 and a4 = 0. In the latter case we prove that Γ is an antipodal cover of a strongly regular graph, which means that it has diameter 4 or 5. For d = 5 the ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2008
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.10.001