Name
Abstract | ||
|---|---|---|
Given a vertex subset C of a distance-regular graph $\Gamma$ on n vertices, it is shown that C is a completely regular code if and only if the number of vertices at maximum distance from C satisfies an expression in terms of the spectrum of $\Gamma$ and some mean numbers computed from the distances among the vertices of C (the so-called "inner distribution" of C). For such codes, this result can be seen as an improvement of Delsarte's linear programming method, since it gives stronger necessary conditions for their existence. As an application, a purely spectral characterization of those distance-regular graphs which are "edge-distance-regular" (that is, with every edge being a completely regular code with the same parameters) is derived. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1137/S0895480100376496 | SIAM J. Discrete Math. |
Keywords | Field | DocType |
algebraic characterization,n vertex,completely regular codes,distance-regular graph,linear programming method,mean number,maximum distance,spectral characterization,distance-regular graphs,vertex subset,stronger necessary condition,regular code,inner distribution,distance regular graph,orthogonal polynomials | Adjacency matrix,Graph theory,Discrete mathematics,Combinatorics,Algebraic number,Vertex (geometry),Orthogonal polynomials,Regular graph,Distance-regular graph,Completeness (statistics),Mathematics | Journal |
Volume | Issue | ISSN |
15 | 1 | 0895-4801 |
Citations | PageRank | References |
6 | 0.63 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. A. Fiol | 1 | 816 | 87.28 |
| E. Garriga | 2 | 164 | 19.92 |