Symmetric squares of graphs
By Koenraad M. R. Audenaert, Chris D. Godsil, G. Royle, Terry Rudolph. 2005
78 citations recorded by the source corpus.
We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of more general graphs. The connection with generic exchange Hamiltonians in quantum mechanics is discussed in Appendix A.
Subfields: Algebra and Number Theory, Mathematical Physics, Algorithms & Complexity
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Citations in the corpus
- The Weisfeiler-Lehman Method and Graph Isomorphism Testing (2011, methodology): “Note that these concepts of k-similarity and k-equivalence were used in [9] (and implicitly in [1]) to demonstrate that any two k-similar graphs have identical k-th symmetric powers, hence addressing the proposition of [3].”
- Non-Isomorphic Graphs with Cospectral Symmetric Powers (2009, background): “Definition 2.1 A pair C = (V,R) is called a coherent configuration or a scheme on V if the following conditions are satisfied: (C1) R∗ contains the diagonal ∆(V ) of the Cartesian product V × V , (C2) R∗ contains the relation RT for all R ∈ R, (C3) given R, S, T ∈ R, the number cR,S(u, v) = |R(u) ∩…”
- Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements (2008, background): “This led Audenaert et al [2] to define the k-th symmetric power X of a graph X : each vertex of X represents a k-subset of vertices of X , and two k-subsets are joined if and only if their symmetric difference is an edge of X .”