Sierpinski垫上连通生成子图的个数
Number of connected spanning subgraphs on the Sierpinski gasket
摘要：
研究了广义Sierpinski垫片$SG_{d,b}(n)$在阶段$n$上的连通生成子图$f_{d,b}(n)$的个数，其中对于$b=2$，$d$的维数为2，3，4;对于$d=2$，$b$的层数为3，4.根据某个阶段的结果导出了具有$b=2,3,4$的$SG_{2,b}(n)$上的渐近增长常数的上、下界，定义为$z_{SG_{d,b}}=\lim_{v \to \infty} \ln f_{d,b}(n)/v$，其中$v$是顶点数.得到了$z_{SG_{d,b}}$的数值。
英文摘要：
We study the number of connected spanning subgraphs $f_{d,b}(n)$ on the generalized Sierpinski gasket $SG_{d,b}(n)$ at stage $n$ with dimension $d$ equal to two, three and four for $b=2$, and layer $b$ equal to three and four for $d=2$. The upper and lower bounds for the asymptotic growth constant, defined as $z_{SG_{d,b}}=\lim_{v \to \infty} \ln f_{d,b}(n)/v$ where $v$ is the number of vertices, on $SG_{2,b}(n)$ with $b=2,3,4$ are derived in terms of the results at a certain stage. The numerical values of $z_{SG_{d,b}}$ are obtained.
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