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基于电网络技巧计数一类平面自相似图的生成树数目

Counting the spanning trees for a class of self-similar planar graphs based on techniques from electrical networks
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摘要 Sierpiński多面体是Sierpiński三角形的三维近似,Sierpiński金字塔自相似图是Sierpiński四面体的1-骨架。本文受Sierpiński金字塔图的构造启发,研究一类构造上极为相似的平面自相似图。基于图的自相似性特点和电网络理论技巧,得到这类自相似图的生成树的计数公式及生成树增长的熵值。 The Sierpinski gasket pyramid networks are the sketches of the Sierpinski tetrahedra which are the three-dimensional analogue of the Sierpinski triangles.Motivated by the construction of Sierpiński gasket pyramid networks,in this work we study the spanning trees of a new class of self-similar planar networks which has a very similar iterative generating method.By using the self-similarity and employing techniques from electrical networks,we obtain the exact analytical expression for the number of spanning trees of this kind of planar networks as well as the entropy of spanning trees.
作者 赵伟良 齐林明 ZHAO Weiliang;QI Linming(Zhejiang Industry Polytechnic College,Shaoxing 312000,Zhejiang,China)
出处 《运筹学学报》 CSCD 北大核心 2022年第4期119-126,共8页 Operations Research Transactions
基金 浙江省教育厅2018年度高校访问学者“教师专业发展项目”(No.FX2018113)。
关键词 Sierpiński三角形 生成树 自相似 电网络等价 熵值 Sierpiński triangle spanning tree self-similar electrically equivalent entropy
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