Godsil-McKay switching and isomorphism

Godsil-McKay switching and isomorphism

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 con...

Godsil-McKay switching and twisted Grassmann graphs

Graph Cospectrality using Neighborhood Matrices

In this note we address the problem of graph isomorphism by means of eigenvalue spectra of different matrix representations: the neighborhood matrix M̂ , its corresponding signless Laplacian QM̂ , and the set of higher order adjacency matrices M`s. We find that, in relation to graphs with at most 10 vertices, QM̂ leads to better results than the signless Laplacian Q; besides, when combined with M̂ ...

Writing Chris Godsil

Some unsolicited advice on writing papers.

Mckay Correspondence

1 Introduction Conjecture 1.1 (since 1992) G ⊂ SL(n, C) is a finite subgroup. Assume that the quotient X = C n /G has a crepant resolution f : Y → X (this just means that K Y = 0, so that Y is a " noncompact Calabi–Yau manifold "). Then there exist " natural " bijections {irreducible representations of G} → basis of H * (Y, Z) (1) {conjugacy classes of G} → basis of H * (Y, Z) (2) As a slogan "...