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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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On relative t-designs in polynomial association schemes
TL;DR: The theory based on the Terwilliger algebra, which is a noncommutative associative semisimple $\mathbb{C}$-algebra associated with each vertex of an association scheme, is developed and a new algebraic characterization of the Hamming schemes is established.
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On the Decoder Error Probability of Rank Metric Codes and Constant-Dimension Codes
Maximilien Gadouleau,Zhiyuan Yan +1 more
TL;DR: The decoder error probability (DEP) of bounded distance decoders (BDDs) forRank metric codes and CDCs, and it is shown that the DEPs for KK codes are the greatest up to a scalar among all CDCs obtained by lifting rank metric codes.
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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: It is proved that S⊆V(G) is in general position if and only if the components of G[S] are complete subgraphs, the vertices of which form an in-transitive, distance-constant partition of S.
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ℓ-distance-balanced graphs
TL;DR: This paper studies a very natural generalization of the concept of distance-balancedness, introduced by Frelih (2014), and obtains some general results on l -distance-balanced graphs and provides various examples.
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The Terwilliger algebras of Johnson graphs
Suogang Gao,Liwei Zhang,Bo Hou +2 more
TL;DR: In this paper, the structure of T under the assumption that m ⩾ 3 and n ⊆ 4 m is the universal enveloping algebra of sl 2, and a C -algebra homomorphism ϑ : U ( sl 2 ) → T is shown to be generated by the image of ϑ and some central elements of T.
References
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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.