منابع مشابه
Hamming Graph in Nomura Algebra
Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of a type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.
متن کاملNomura algebras of nonsymmetric Hadamard models
Spin models for link invariants were introduced by Jones [7], and their connection to combinatorics was revealed first in [4]. Jaeger and Nomura [6] constructed nonsymmetric spin models for link invariants from Hadamard matrices, and showed that these models give link invariants which depend nontrivially on link orientation. These models are a modification of the Hadamard model originally const...
متن کاملElusive Codes in Hamming Graphs
We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length...
متن کاملIsometric embeddings in Hamming graphs
The results presented in this paper are parts of my doctoral thesis [ 193; the algorithm and some of the characterizations in Section 7 have been introduced in [ 181. Motivation for isometric embeddings into Hamming graphs has come from communication theory (Graham and Pollak [ 121) an-d linguistics (Firsov 1181). Isometric subgraphs of Hamming graphs also appear in biology as “quasi-species” (...
متن کاملNILPOTENT GRAPHS OF MATRIX ALGEBRAS
Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.01.020