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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
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Subgroup perfect codes in Cayley graphs
TL;DR: It is proved that a group is code-perfect if and only if it has no elements of order $4 and all subgroup perfect codes in any generalized quaternion group are determined.
Journal ArticleDOI
A new inequality for bipartite distance-regular graphs
TL;DR: It is shown that θ is three-term recurrent (or TTR) whenever (i)-(iii) are satisfied, and formulae for the intersection numbers and eigenvalues of Γ are found in terms of at most two free parameters.
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A note on adjacency preservers on hermitian matrices over finite fields
TL;DR: It is shown that any map which preserves adjacency on hermitian matrices over a finite field is necessary bijective and hence of the standard form.
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On subgroup perfect codes in Cayley graphs
Junyang Zhang,Sanming Zhou +1 more
TL;DR: A subgroup perfect code of a Cayley graph is defined in this article, where the identity element is the product of an element of a tiling of a group G and a subgroup H of G such that every element of G can be expressed as a product of H and A of G.
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The Search for Pseudo Orthogonal Latin Squares of OrderSix
TL;DR: In this article, the complete computer search for a strongly regular graph with parameters (36,15,6,6) and chromatic number six was conducted and the result is that no such graph exists.
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.