带权图的多重分形研究

刘胜久,李天瑞,珠杰,刘佳

Research on multi⁃fractals of weighted graphs

Shengjiu Liu,Tianrui Li,Jie Zhu,Jia Liu

表4 节点权重为复数的四种不同类型带权图分形维数统计表

Table 4 Statistics of fractal dimensions of four weighted graphs with node weight being complex numbers

编号	节点权重	边权重	分形维数
1	复数 $(a + b i) f (v)$	正实数 $f (e)$	$\frac{1}{l g \sqrt[]{a^{2} + b^{2}} e^{i t a n^{- 1} \frac{b}{a}} \sum_{v \in V} f (v)} l g \sum_{e \in E} f (e)$ (45)
2		负实数 $- f (e)$	$\frac{1}{l g \sqrt[]{a^{2} + b^{2}} e^{i t a n^{- 1} \frac{b}{a}} \sum_{v \in V} f (v)} l g e^{i π} \sum_{e \in E} f (e)$ (46)
3		纯虚数 $i f (e)$	$\frac{1}{l g \sqrt[]{a^{2} + b^{2}} e^{i t a n^{- 1} \frac{b}{a}} \sum_{v \in V} f (v)} l g e^{\frac{i π}{2}} \sum_{e \in E} f (e)$ (47)
4		复数 $(a + b i) f (e)$	$\frac{1}{l g \sqrt[]{a^{2} + b^{2}} e^{i t a n^{- 1} \frac{b}{a}} \sum_{v \in V} f (v)} l g \sqrt[]{a^{2} + b^{2}} e^{i t a n^{- 1} \frac{b}{a}} \sum_{e \in E} f (e)$ (48)