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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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The extended 1-perfect trades in small hypercubes
TL;DR: Using a computer-aided approach, all Steiner trades with parameters ( 5, 6, 12 ) are classified and nonequivalent primary extended 1 -perfect trades of length 10, constant-weight extended 1-perfect tradesof length 12 , and Steiner trade derived from them are classified.
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On the connectedness of the complement of a ball in distance-regular graphs
TL;DR: In this article, it was shown that the second subconstituent of any primitive strongly regular graph is always connected, and this property can be generalized to distance-regular graphs, where the standard sequence corresponding to the second largest eigenvalue of the graph changes sign.
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Binary codes from the line graph of the n-cube
TL;DR: A regular subgroup of the automorphism group that can be used for permutation decoding, or partial permutation decode, for any information set is found.
Edge-Transitive Homogeneous Factorisations of Complete Graphs
TL;DR: In this paper, the authors studied edge-transitive homogeneous factorisations of complete graphs and gave necessary and sufficient arithmetic conditions on certain parameters for such factorisations to exist, and gave two constructions of infinite families of examples where they specify the parameters explicitly.
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Full automorphism group of the generalized symplectic graph
TL;DR: The generalized symplectic graph GS p 2 ν ( q,m ) relative to K over F q is introduced in this paper, which is the graph with m -dimensional totally isotropic subspaces of the 2 −dimensional symplectic space F q (2 ν ) as its vertices.
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.