A Polynomial Invariant of Graphs On Orientable Surfaces

  title={A Polynomial Invariant of Graphs On Orientable Surfaces},
  author={B. Bollob{\'a}s and O. Riordan},
  journal={Proceedings of The London Mathematical Society},
Our aim in this paper is to construct a polynomial invariant of cyclic graphs, that is, graphs with cyclic orders at the vertices, or, equivalently, of 2-cell embeddings of graphs into closed orientable surfaces. We shall call this invariant the cyclic graph polynomial, and denote it by the letter C . The cyclic graph polynomial is a three-variable polynomial which generalizes the Tutte polynomial in an essential way. In the next section we de®ne cyclic graphs from two different viewpoints, and… Expand

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