•  
  •  
 

Keywords

Godsil-McKay switching; Spectral characterization; Cospectral graphs; Graph isomorphism; Graph products.

Abstract

Godsil-McKay switching is an operation on graphs that doesn’t change the spectrum of the adjacency matrix. Usually (but not always) the obtained graph is non-isomorphic with the original graph. We present a straightforward sufficient condition for being isomorphic after switching, and give examples which show that this condition is not necessary. For some graph products we obtain sufficient conditions for being non-isomorphic after switching. As an example we find that the tensor product of the grid L(ℓ,m) (ℓ > m>2) and a graph with at least one vertex of degree two is not determined by its adjacency spectrum.

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.