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Z—Transformation Graphs of perfect Matchings of Hexagonal Systems

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【作者】 张福基郭晓峰陈荣斯

【Author】 Zhang Fuji, Guo Xiaofong and Chen Rongsi Department of Mathematics, Xinjiang University

【摘要】 <正> A hexagonal system is defined to be a finit connected plane graph with no cut-vertices in which every interior region is surrounded by a regular hexagon of side length one.In the present paper we define the Z-transformation graph of a hexagonal system H to be the graph where vertices are the perfect matchings of (?) and where two perfect matchings are joint by an edge provided their symmetric difference is a hexagon of H.We prove that,if H has perfect matchings,Z(H)is a connected bipartite graph.Besides,Z(H)is either an elementary chain or a graph with girth 4.Some further results are obtained also.

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