On bipartite distance-regular graphs with a strongly closed subgraph of diameter three
نویسندگان
چکیده
منابع مشابه
Bipartite regular graphs with fixed diameter
For given nonnegative integers k and D , we consider the problem of determining n,(k, D ) , the smallest number n for which there exists a k-regular bipartite graph on n vertices with diameter D . We solve the problem for all pairs ( k , D ) with D + 2 (mod 4) and D + 3 (mod 4), for all pairs ( k , D ) with k even or k prime and D + 3 (mod 4), for all pairs with D I 9 or k I 4, and for a few ot...
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Let Γ denote a bipartite Q-polynomial distance-regular graph with vertex set X, diameter d ≥ 3 and valency k ≥ 3. Let RX denote the vector space over R consisting of column vectors with entries in R and rows indexed by X. For z ∈ X, let ẑ denote the vector in RX with a 1 in the z-coordinate, and 0 in all other coordinates. Fix x, y ∈ X such that ∂(x, y) = 2, where ∂ denotes path-length distance...
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Article history: Received 9 April 2013 Accepted 15 December 2013 Available online 13 January 2014 Submitted by R. Brualdi
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Let Γ denote a bipartite distance-regular graph with diameter D. In [J. S. Caughman, Bipartite Q-polynomial distance-regular graphs, Graphs Combin. 20 (2004), 47–57], Caughman showed that if D > 12, then Γ is Q-polynomial if and only if one of the following (i)-(iv) holds: (i) Γ is the ordinary 2D-cycle, (ii) Γ is the Hamming cube H(D, 2), (iii) Γ is the antipodal quotient of the Hamming cube H...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.08.019