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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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Dynamic Cage Survey
Geoffrey Exoo,Robert Jajcay +1 more
TL;DR: In this paper, the results of over 50 years of searches for cages are presented, along with the important theorems, list all the known cages, compile tables of current record holders, and describe in some detail most of the relevant constructions.
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Efficient reconstruction of sequences
TL;DR: The smallest N such that N erroneous versions always suffice to reconstruct a sequence of length n, either exactly or with a preset accuracy and/or with a given probability is introduced.
Journal ArticleDOI
Explicit construction of graphs with an arbitrary large girth and of large size
Felix Lazebnik,V. A. Ustimenko +1 more
TL;DR: This paper gives an explicit construction of a q -regular bipartite graph on v = 2 q k vertices with girth g ⩾ k + 5 which is the incidence graph of a flag-transitive semiplane.
Some algebra related to P - and Q -polynomial association schemes.
TL;DR: In this paper, the authors consider a pair of linear transformations A : V → V and A :V → V satisfying the following four conditions: (i) A and V are both diagonalizable on V, (ii) A is both diagonalisable on V and V is both diagonalizable on A, and (iii) there is no subspace W of V such that both AW ⊆ W, AW⊆ AW, AW ∆ W, other than W = 0 and W = V.
Proceedings ArticleDOI
Two relations that generalize the $q$-Serre relations and the Dolan-Grady relations
TL;DR: The Tridiagonal algebra as discussed by the authors is an algebra on two generators which is defined as follows: a field is a field, and a sequence of scalars taken from a field can be represented by two symbols A and A. The corresponding Tridiagonal algebra T is the associative K-algebra with 1 generated by A. In the first part of this paper, we survey what is known about irreducible finite di-mensional T-modules.
References
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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.