Adjacency algebra

In algebraic graph theory, the adjacency algebra of a graph G is the algebra of polynomials in the adjacency matrix A(G) of the graph. It is an…

Papers overview

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2018

We can define the adjacency algebra of an association scheme over an arbitrary field. It is not always semisimple over a field of…

2014

We compare the duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the…

2013

A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a…

2010

Forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph X contains a Hadamard…

2008

It is well known that the adjacency algebra of an association scheme has the standard character. In this paper we first define…

2008

In this paper, we investigate semisimplicity of cellular algebras over positive characteristic fields. Our main result shows that…

2005

It is well-known that a connected finite simple graph is regular if and only if the all-ones matrix spans an ideal of its…

2004

To each association scheme G and to each field R, there is associated naturally an associative algebra, the so-called adjacency…

2002

In the book entitled "Methods of Representation Theory" by Curtis and Reiner they discuss character tables of Hecke algebras…

1986

In order to study graphs, the notion of graph must first be defined. A graph is a set of points (called vertices, or nodes) and a…