Emms, Hancock, Severini and Wilson's spectral characterization conjecture for strongly regular graphs

About 15 years old · traced to

Let GG and HH be strongly regular graphs with the same set of parameters. For a graph FF, let U(F){\bf U}(F) denote its transition matrix, let U(F)3{\bf U}(F)^3 be its third power, let (U(F)3)+({\bf U}(F)^3)^+ denote its positive support, and let SpecSpec denote the spectrum. Emms, Hancock, Severini and Wilson's conjecture.

G≅H⟺Spec((U(G)3)+)=Spec((U(H)3)+).G \cong H \quad\Longleftrightarrow\quad Spec\bigl(({\bf U}(G)^3)^+\bigr)=Spec\bigl(({\bf U}(H)^3)^+\bigr).

The conjecture proposes that, within a fixed parameter set of strongly regular graphs, the spectrum of the positive support of the cube of the transition matrix distinguishes isomorphic graphs. The supplied source does not state whether the conjecture has been resolved.

References

Primary source

Norio Konno and Iwao Sato, “On the relation between quantum walks and zeta functions”, arXiv:1103.0079 (2011).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.