Eigenvectors of Distance-Regular Graphs,

Abstract

The objective of this work is to find properties of a distance-regular graph G that are expressed in the eigenvectors of its adjacency matrix. The approach is to consider the rows of a matrix of orthogonal eigencolumns as (coordinates of) points in euclidean space, each one corresponding to a vertex of G. For the second eigenvalue, the symmetry group of the points is isomorphic to the automorphism group of G. Adjacency of vertices is related to linear dependence, linear independence and proximity of points. Relative position of points studied by way of the polytope that is their convex hull. Several families of examples are included.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA185375

Entities

People

  • David L. Powers

Organizations

  • Clarkson University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Coefficients
  • Computer Science
  • Diameters
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Graph Theory
  • Mathematical Analysis
  • Mathematics
  • Matrix Theory
  • New York
  • Permutations
  • Polynomials
  • Symmetry
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space