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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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Book ChapterDOI
Improved Quantum Information Set Decoding
TL;DR: This paper gives an alternative view on the quantum walk based algorithms proposed by Kachigar and Tillich (PQCrypto'17) and translates May-Ozerov Near Neighbour technique (Eurocrypt'15) to an `update-and-query' language more suitable for the quantumWalk framework.
Journal ArticleDOI
On distance-regular Cayley graphs on abelian groups
Štefko Miklavič,Primo Šparl +1 more
TL;DR: The complete classification of distance-regular Cayley graphs Cay(G;S) for such pairs of G and S is obtained.
Journal ArticleDOI
Some Applications of the Proper and Adjacency Polynomials in the Theory of Graph Spectra
TL;DR: An upper bound for the cardinality of k (u) is derived, showing that j k (U)j decreases at least as O( 2 ), and the cases in which the bound is attained are characterized.
Journal ArticleDOI
Hyperbolic lines in generalized polygons
TL;DR: In this paper, the theory of hyperbolic lines in generalized polygons was developed, and the extremal situation where the lines are long was investigated. But it was not shown that the existence of long lines in the generalized quadrangles is a special case of the generalized hexagons.
Journal ArticleDOI
The independence number for polarity graphs of even order planes
Sylvia A. Hobart,Jason Williford +1 more
TL;DR: In this paper, the authors used coherent configurations to obtain new upper bounds on the independence number of orthogonal polarity graphs of projective planes of even order, and these bounds differ only by 1 from the size of the largest known independent sets.
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.