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Regularity and the generalized adjacency spectra of graphs
- Source :
-
Linear Algebra & its Applications . Jul2006, Vol. 416 Issue 2/3, p1033-1037. 5p. - Publication Year :
- 2006
-
Abstract
- Abstract: For every rational number x ∈(0,1), we construct a pair of graphs, one regular and one nonregular with adjacency matrices A 1 and A2, having the property that A 1 − xJ and A 2 − xJ have the same spectrum (J is the all-ones matrix). This solves a problem of Van Dam and the second author. For some values of x, we have generated the smallest examples (with respect to the number of vertices) by computer. [Copyright &y& Elsevier]
- Subjects :
- *EIGENVALUES
*GRAPH theory
*MATRICES (Mathematics)
*UNIVERSAL algebra
*REAL numbers
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 416
- Issue :
- 2/3
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 21052485
- Full Text :
- https://doi.org/10.1016/j.laa.2006.01.026