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Distance-Regular Graphs
TLDR
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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The girth of a thin distance-regular graph
TL;DR: The graph Γ isthin if for each vertexx of Γ, every irreducibleT(x)-module is thin and c3=1.
Two problems on homogeneous structures, revisited
TL;DR: It is shown, following a suggestion of Peter Cameron (1996), that while strongly regular graphs provide some interesting examples, one must look beyond this class in general for the desired approximations.
Journal ArticleDOI
Cores of Geometric Graphs
Chris Godsil,Gordon F. Royle +1 more
TL;DR: In this paper, it was shown that rank-three graphs are either cores or complete cores, and they showed that this holds for all strongly regular graphs, including the block graphs of Steiner systems and orthogonal arrays.
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Characterization of general position sets and its applications to cographs and bipartite graphs
Bijo S. Anand,S V Ullas Chandran,Manoj Changat,Sandi Klavžar,Sandi Klavžar,Sandi Klavžar,Elias John Thomas +6 more
TL;DR: In this article, it was shown that a vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position sets of G is the general position number gp(G) of G. If G is bipartite, then gp (G) is the maximum of ω(G), and the maximum order of an induced complete multipartite subgraph of the complement of G can be determined in polynomial time.
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The Eigenspaces of the Bose-Mesner-Algebras of the AssociationSchemes Corresponding to Projective Spaces and Polar Spaces
TL;DR: These eigenspaces and the eigenvalues are determined for projective spaces and for polar spaces, which allows characterizations of certain sets of subspaces of these geometries.
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.