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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 graphs of projective codes
TL;DR: It is shown that the graph $\Pi(n,k)_q$ is connected, its diameter is equal to the diameter of the Grassmann graph and the distance between any two vertices coincides with the distance around these vertices in the Grassman graph.
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Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learning
TL;DR: A general class of structure-related features, termed Distance Encoding (DE), that assists GNNs in representing any set of nodes, while providing strictly more expressive power than the 1-WL test and significantly outperform other state-of-the-art methods especially designed for the above tasks.
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Four-class skew-symmetric association schemes
Jianmin Ma,Kaishun Wang +1 more
TL;DR: This paper characterize and classify 4-class imprimitive skew-symmetric association schemes, and proves that none of 2-class Johnson schemes admits a 4- class skew-Symmetric fission scheme.
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Augmented down-up algebras and uniform posets
TL;DR: The notion of augmented down-up (or ADU) algebras was introduced in this paper, motivated by the structure of the uniform posets and the main inspiration for the ADU algebra concept comes from the second author's thesis concerning a type of uniform poset constructed using a dual polar graph.
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Multidiameters and Multiplicities
TL;DR: The k -diameter of a graph ?
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.