Gauss-Bonnet Formula, Finiteness Condition, and Characterizations of Graphs Embedded in Surfaces

@article{Chen2008GaussBonnetFF,
  title={Gauss-Bonnet Formula, Finiteness Condition, and Characterizations of Graphs Embedded in Surfaces},
  author={Beifang Chen and Guantao Chen},
  journal={Graphs and Combinatorics},
  year={2008},
  volume={24},
  pages={159-183}
}
Let G be an infinite graph embedded in a closed 2-manifold, such that each open face of the embedding is homeomorphic to an open disk and is bounded by finite number of edges. For each vertex x of G, define the combinatorial curvature KG(x) = 1− d(x) 2 + ∑ σ∈F (x) 1 |σ| as that of [9], where d(x) is the degree of x, F (x) is the multiset of all open faces σ in the embedding such that the closure σ̄ contains x (the multiplicity of σ is the number of times that x is visited along ∂σ), and |σ| is… CONTINUE READING
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References

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Showing 1-10 of 17 references

Introduction to Graph Theory, 2nd ed

  • D. West
  • First version: June,
  • 2001
1 Excerpt

Digital curvature flow of planar digital curve, in “Free boundary problems: theory and applications II

  • A. Imiya, U. Eckhardt
  • (Chiba,
  • 1999
1 Excerpt

Combinatorics of triangulations of 3-manifolds

  • F. Luo, R. Stong
  • Trans. Amer. Math. Soc
  • 1993
2 Excerpts

The Gram-Sommerville and Gauss-Bonnet theorems and the combinatorial geometric measures for noncompact polyhedra

  • B. Chen
  • Advances in Math
  • 1992
1 Excerpt

Pseudo-curvature of a graph, Lecture at ‘Workshop on topological graph theory

  • M. Ishida
  • Yokohama National University,
  • 1990
1 Excerpt

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