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Embedding and the first Laplace eigenvalue of a finite graph

Author

Listed:
  • Takumi Gomyou

    (Osaka University)

  • Toshimasa Kobayashi

    (Setsunan University)

  • Takefumi Kondo

    (Kagoshima University)

  • Shin Nayatani

    (Nagoya University)

Abstract

Göring–Helmberg–Wappler introduced optimization problems regarding embeddings of a graph into a Euclidean space and the first nonzero eigenvalue of the Laplacian of a graph, which are dual to each other in the framework of semidefinite programming. In this paper, we introduce a new graph-embedding optimization problem, and discuss its relation to Göring–Helmberg–Wappler’s problems. We also identify the dual problem to our embedding optimization problem. We solve the optimization problems for distance-regular graphs and the one-skeleton graphs of the $$\textrm{C}_{60}$$ C 60 fullerene and some other Archimedian solids.

Suggested Citation

  • Takumi Gomyou & Toshimasa Kobayashi & Takefumi Kondo & Shin Nayatani, 2024. "Embedding and the first Laplace eigenvalue of a finite graph," Journal of Combinatorial Optimization, Springer, vol. 48(1), pages 1-24, August.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:1:d:10.1007_s10878-024-01191-1
    DOI: 10.1007/s10878-024-01191-1
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