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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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Error graphs and the reconstruction of elements in groups
TL;DR: This paper defines error graphs and investigates their basic properties and obtains a complete solution of the above problems for the transposition Cayley graph on the symmetric group.
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Exceptional graphs with smallest eigenvalue -2 and related problems
TL;DR: In this article, the authors summarized the known results on graphs with smallest eigenvalue around -2, and completed the theory by proving a number of new results, giving comprehensive tables of the finitely many exceptions, and posing some new problems.
Journal ArticleDOI
Potential Theory on Distance-Regular Graphs
TL;DR: A graph may be regarded as an electrical network in which each edge has unit resistance and explicit formulae for the effective resistance of the network when a current enters at one vertex and leaves at another in the distance-regular case are obtained.
Journal ArticleDOI
Association schemes based on attenuated spaces
Kaishun Wang,Jun Guo,Fenggao Li +2 more
TL;DR: A family of symmetric association schemes are obtained which are a common generalization of the Grassmann schemes and the bilinear forms schemes, and all the parameters of the association scheme are computed.
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On non-antipodal binary completely regular codes
TL;DR: It is concluded that there are no unknown nontrivial non-antipodal completely regular binary codes with minimum distance d>=3 and there are new such codes with covering radius @r=6 and 7.
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.