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Cospectral graphs and the generalized adjacency matrix
- Source :
-
Linear Algebra & its Applications . May2007, Vol. 423 Issue 1, p33-41. 9p. - Publication Year :
- 2007
-
Abstract
- Abstract: Let J be the all-ones matrix, and let A denote the adjacency matrix of a graph. An old result of Johnson and Newman states that if two graphs are cospectral with respect to yJ − A for two distinct values of y, then they are cospectral for all y. Here we will focus on graphs cospectral with respect to yJ − A for exactly one value of y. We call such graphs -cospectral. It follows that is a rational number, and we prove existence of a pair of -cospectral graphs for every rational . In addition, we generate by computer all -cospectral pairs on at most nine vertices. Recently, Chesnokov and the second author constructed pairs of -cospectral graphs for all rational , where one graph is regular and the other one is not. This phenomenon is only possible for the mentioned values of , and by computer we find all such pairs of -cospectral graphs on at most eleven vertices. [Copyright &y& Elsevier]
- Subjects :
- *MATRICES (Mathematics)
*REAL numbers
*GRAPH theory
*SPECTRUM analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 423
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 24388128
- Full Text :
- https://doi.org/10.1016/j.laa.2006.07.017