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Distance-Regular Graphs
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In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.Abstract:
Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distanceread more
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Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs
Kris Coolsaet,Aleksandar Jurišić +1 more
TL;DR: It is proved the nonexistence of a distance-regular graph with intersection array {74,54,15;1,9,60} and of distance- regular graphs with intersection arrays {4r^3+8r^2+6r+1,2r(r+ 1),2r^ 2+2 r+1; 1,2 r(r-1),(2r+2))(2 r-1)(2r-2)+1);
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An Eigenvalue Characterization of Antipodal Distance-Regular Graphs
TL;DR: It is shown that is an r-antipodal distanceregular graph if and only if the distance graph d is constituted by disjoint copies of the complete graph Kr, with r satisfying an expression in terms of n and the distinct eigenvalues.
Journal ArticleDOI
To the theory of q -ary Steiner and other-type trades
TL;DR: A one-to-one correspondence is shown between the clique bitrades that meet the weight-distribution lower bound on the cardinality and the bipartite isometric subgraphs that are distance-regular with certain parameters.
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On the metric dimension of bilinear forms graphs
Min Feng,Kaishun Wang +1 more
TL;DR: An improvement on Babai's most general bound for the metric dimension of distance-regular graphs, in the case of H"q(n,d) with n>=d>=4.
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Spin models for link polynomials, strongly regular graphs and Jaeger's Higman-Sims model.
TL;DR: In this paper, the authors consider a spin model for link invariants, which involves the Higman-Sims graph and the Kauffman polynomials for links, and give an exposition of a recent spin model due to F. Jaeger.
References
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Journal ArticleDOI
Equilateral point sets in elliptic geometry
J.H. van Lint,J.J. Seidel +1 more
TL;DR: In this paper, the authors highlight equilateral point sets in elliptic geometry and show that Paley's construction may be reversed to obtain a C -matrix of order 46, in view of the existence of a Hadamard matrix of order 92.
BookDOI
On construction and identification of graphs
TL;DR: The problem of graph identification has been studied in the theory of permutation groups for a long time, see as mentioned in this paper for a discussion of the main points of the problem and an algorithm for graph identification.