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The number of spanning trees of plane graphs with reflective symmetry |
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| Authors: | Mihai Ciucu Fuji Zhang |
| Institution: | a School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA b School of Sciences, Jimei University, Xiamen 361021, PR China c Department of Mathematics, Xiamen University, Xiamen 361005, PR China |
| Abstract: | A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G. |
| Keywords: | 05C80 |
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