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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
Citations
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Max-cut and extendability of matchings in distance-regular graphs
TL;DR: It is proved that all distance-regular graphs with diameter D ≥ 3 are 2-extendable and several better lower bounds are obtained for the extendability of distance- regular graphs of valency k ≥ 3 that depend on k, λ and μ and the inequalities are incomparable with known eigenvalue bounds for these combinatorial parameters.
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On cyclotomic schemes over finite near-fields
TL;DR: In this paper, a cyclotomic association scheme over a finite near-field is introduced, and it is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V), where V is the linear space associated with K.
Spectral Characterization of Generalized Cocktail-Party Graphs
Jianfeng Wang,Qiongxiang Huang +1 more
TL;DR: In this paper, it was shown that all generalized cocktail-party graphs with order at least 23 are determined by their adjacency spectra, i.e., they can be characterized by their spectral properties.
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Notes on the Leonard System Classification
TL;DR: This paper gives a proof of isomorphism of Leonard systems that is shorter and involves minimal computation and gives a comprehensive description of the intersection numbers of a Leonard system.
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The symbiotic relationship of combinatorics and matrix theory
TL;DR: In this paper, the authors demonstrate the mutually beneficial relationship that exists between combinatorics and matrix theory, and demonstrate the mutual benefit of combinatorial and matrix theoretic models.
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.