The number of spanning trees of plane graphs with reflective symmetry

Authors:
Mihai Ciucu;Weigen Yan;Fuji Zhang
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA;School of Sciences, Jimei University, Xiamen, PR China;Department of Mathematics, Xiamen University, Xiamen, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

Citing 5
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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 the number of spanning trees of two smaller graphs. each of which has about half the number of vertices of G.